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Alrighty... Long post incoming!

Gobada = He walked together. You can use this if you just reword the sentence slightly:
Aragorn a adan gaeleb gobada na Imladris = Aragorn and a sick man walked together to Rivendell
Do you mean 'a man of the race of man' by the way? If you just mean 'a man' as the opposite of 'a woman' then use benn. It sounds a little odd as Aragorn is also of the Race of Man (albeit the Dúnedain branch of it).
You forgot mutation on Caeleb, but in this case I don't think I'd use it as it means 'bedridden', i.e. he wouldn't be walking anywhere! I'd use Lhaew = Sickly, ill.

Govadar edhel -> Covar edhel = They meet an Elf. Guessing you're using Govada- from Thorsten's course instead of the later more accurate Cova- = to meet?

Man eneth lîn -> Man i eneth lîn. Don't forget the definite article, it's not optional unless we're writing poetry, and if we're using the formal 'thy' instead of the informal 'gîn' you wouldn't leave it out.

Tegin vellon nîn na Imladris, e caeleb -> Tegin mellonenin/melloneg na Imladris. Sâf cael.
Your sentence literally translates as 'I am bringing my friend (who I own) to Imladris. He is sickness (as in he literally is something called sickness). E is an emphatic pronoun and isn't the same as the English verb 'to be', though it's easy to confuse them. My reworded sentence says 'I am bringing my friend/dear friend to Imladris. He has a sickness.'

I know it's ingrained in a lot of people by now because it was used in the films, but you wouldn't say mellon nîn as it implies possession. -enen is the possessive suffix (in the Lord of the Rings, Gandalf says Lammen = my tongue) and -eg is a diminutive suffix, meaning 'my little friend, my dear friend'.

Pelin tulu -> Boe rethol?
Pelin is either the verb Pel- = to fade, Pelin = I fade or the reconstructed Pol- = to be able to which I prefer to render as Polin = I can but would also possibly appear as the homophone Pelin = I can.
Tulu = 'Support, prop' as in a beam that supports weight.
So this either says "I fade a support" or "I can a support".

There are various ideas on how to say 'help'. Alia- = to help, bless. Reth- or Reitha- = to save (from edraith = saving). Atha- = to ease, to help. They're all reconstructed.
My version is Boe rethol? = Dost thee need help? (Or Boe reithol? = Dost thee need help?).

Ma -> either Boe rethin/Boe reithon = I need help or Ná = Yes
I'm aware Renk uses Ma to mean 'Yes' but it doesn't. It's an interjection that only means 'good' and is archaic. If you want to agree with something, repeat the question but change the tense (so here, we have "Do you need help?" "I need help.") Ná is a reconstruction based on common sense and Quenya from the verb Na-.

Gobada ven a dago hain -> either Gobado adh ven a dhago hain! or Tolo adh ven a dhago hain!
Gobado adh ven a dhago din! = Walk together with us and slay them
Tolo adh ven a dhago din! = Come with us and slay them
Remember 'a' causes soft mutation.
(T)Din = Them. Hain = Those.

Mae -> sounds like an attempt at the English 'okay'? I suppose the subject could be missing and the Elf is saying "(It is) well".

Mellon gîn fîr -> You've switched from the formal to informal. Is this intended? Either way swap Mellon gîn to either Mellonegen or Mellonelen.

Aduial tel min Ennorath -> Aduial tôl na Ennorath
min = in the
tôl = it comes

Ma, ha ennas! -> Ma, de ennas
Ha = an old Noldorin pronoun
(t)De = it is. Modern Sindarin.

Hannon, Eglerion -> Gin/Len hannon, Eglerion.
Need a pronoun otherwise you're saying 'I thank Eglerion'.

1) In Noldorin Lhaew = Frequent, many and Thlaew = sick, ill. In modern Sindarin Lhaew -> Laew and Thlaew ->Lhaew.
2) Parma Eldalamberon #17, in a discussion about Tolkien's final decision on what Mae G'ovannen meant. Page 158 - from the root KOB/KOM, S. Cova- come together, meet.
3) în is a reflexive pronoun from the King's Letter "Ar e aníra ennas suilannad mhellyn în phain" = And he desires a meeting of all his own friends. We know that these are possessive from the following attested phrases:
Alae! ered en Echoriath, ered e·mbar nín = Alas! Mountains of Echoriath, mountains of my home
Caro den i innas lîn = Thy will be done
i mbas ilaurui vín = Our daily bread
4) It's the same pronunciation, I just favour using 'f' over 'v'.
5) Stylistic difference! "He is 'something called sick'" then.
6) The only glossed meaning is 'together'. Admittedly if you're doing something together with someone you are doing it 'with' someone, so perhaps you could leave out the preposition.
7) 'Them' and 'those' are only the same word in some English dialects, and most people would say it's 'wrong'. "Them apples" is hardly Standard English! Din is the plural of Den. It -> Them.
8) Given the lack of a concrete way of saying 'yes', I'm not convinced other than through hand movements they would show agreement in the same way we do in English. (Ask not an Elf a question for they will say both yes and no!)
9) Extrapolation from the object pronoun den. All pronouns in Sindarin follow a pattern. Attested are in bold, extrapolations are in italics. The order is nominative -> object -> possessive and this is before soft mutation has been applied, these are the base forms.

Ni -> Nin -> Nîn = I am -> Me -> My
Le -> Len -> Lîn = Thou art -> Thee -> Thy/Thine
De -> Den -> Dîn = You are -> You -> Your (Doriathrin)
Ci -> Cin -> Cîn = You are -> You -> Your (Informal modern Sindarin)
Te -> Ten -> Tîn = He/she/it is -> Him/her/it -> Their
Se -> Sen -> Sin = This is -> This -> These
Sa -> San -> Sain = That is -> That -> Those

Er... what? They're glossed as possessive pronouns, their meanings are quite distinct from the nominative and the object, and they act as adjectives as they take soft mutation. We also have the emphatic pronouns (Im, Ech, E/Est) which are attested (Hollin Gate inscription and PE/17), and again Tolkien specifically stated that is what they were. The only ones people have ever argued over are 'den' in 'caro den' and 'în' in the King's Letter. The others are all well glossed and translated by Tolkien.

nîn = my in Vinyar Tengwar #44 and Unfinished Tales
lîn = thy in Vinyar Tengwar #44
mín = our in Vinyar Tengwar #44 (There's a theme, these three are all in the Lord's Prayer )
sín = these from the Hollin Gate inscription (Celebrimbor o Eregion teithant i thiw hín)

The use of the direct object with the pronoun (i thiw hín = 'the letters these', these letters; i eneth lín = 'the name thy', thy name etc.) is identical to Welsh grammar where the possessive pronoun is an adjective following the noun and the noun is preceded by the direct object (y ty tau = thy house). Sindarin is well known for having its grammar based on Welsh.

As I tried to illustrate with the wee table, Sindarin pronouns follow patterns. Object pronouns have an -n suffix (nin, len, den, ten etc.), the vowel lengthens for possession, and the -n suffix disappears for the nominative (ni, ci). Thus it's not much of a leap to say from den = it, you remove the suffix -n to give you te = he/she/it (we know it's not de = he/she/it because den has undergone soft mutation as the object of Caro).

I would say Aragorn tiria/tîr na i Ithil = Aragorn gazes at the moon
Anin is 'to/for the' not 'at the', so it wouldn't mean the same thing if you used it.

I would follow Tolkien's names for places (Bar-in-Gwael, Bar-in-Mŷl) and say Bar Bangad = House of trading or Bar-i-Mbaich = House of goods.

The verb for 'to trade' is Banga-. Bangon = I buy, I trade, etc.

I was giving you an example of a place name without an attached article (like Amon Sûl, Rath Celerdain - these don't show mutation either).
If you want it with attached article, Banga has an MB root:
Bar-e-Mbangad = House of the trading