Oui, et j’ai aussi de la colle.

Because French normally avoids having je directly before a vowel sound.
So je becomes j’ before verbs like ai:

• je ai → j’ai
• je aime → j’aime
• je habite → j’habite

This is called elision.

Ai is the 1st person singular form of the verb avoir (to have) in the present tense.

So:

• j’ai = I have

The full present tense of avoir is:

• j’ai = I have
• tu as = you have
• il/elle a = he/she has
• nous avons = we have
• vous avez = you have
• ils/elles ont = they have

French usually needs an article before a noun. Here colle means glue as an uncountable substance, so French uses the partitive article:

• du for masculine singular nouns
• de la for feminine singular nouns
• de l’ before a vowel or mute h
• des for plural nouns

So:

• de la colle = some glue

You normally would not just say j’ai aussi colle.

Because une colle usually means one glue item or a specific type/container of glue, while de la colle means some glue in a general substance sense.

Compare:

• J’ai de la colle. = I have some glue.
• J’ai une colle. = I have a glue / one glue item.
  This is possible in certain contexts, but it is less natural if you simply mean the material.

So de la colle is the normal choice for some glue.

Yes, colle is feminine. You can tell because the sentence uses la:

• de la colle

That tells you the noun is feminine singular.

So if you want to say the glue, it would be:

• la colle

Aussi means also or too.

In j’ai aussi de la colle, it comes after the verb:

• j’ai aussi = I also have

This is a very common placement in French.

You may also hear:

• J’ai de la colle aussi.

That also means I have glue too, but the emphasis is a little different.
In your sentence, aussi is naturally attached to the idea of having.

They do different jobs:

• et = and
• aussi = also / too

So:

• Oui, et j’ai aussi de la colle.
  = Yes, and I also have some glue.

Here et connects this statement to what came before, while aussi adds the meaning of also.

Yes. That would also be correct.

• Oui, j’ai aussi de la colle. = Yes, I also have some glue.
• Oui, et j’ai aussi de la colle. = Yes, and I also have some glue.

Adding et makes it sound more connected to a previous sentence or idea.

A simple pronunciation guide is:

• Oui → wee
• et → ay
• j’ai → roughly zhay
• aussi → oh-see
• de la → duh la
• colle → koll

So the whole sentence sounds roughly like:

wee ay zhay oh-see duh la koll

More accurately in IPA:

/wi e ʒe o.si də la kɔl/

No special liaison is made here. Et is pronounced simply as /e/, and then j’ai begins normally:

• et j’ai → /e ʒe/

So you do not pronounce a t sound between them.

In a basic negative sentence, the partitive article usually changes to de (or d’ before a vowel).

So:

• J’ai de la colle. = I have some glue.
• Je n’ai pas de colle. = I don’t have any glue.

That change is very important and very common in French.

Yes. In some contexts, une colle can also mean things like:

• a very difficult question
• a quiz/test (in some school contexts)

But in de la colle, the meaning is clearly the substance glue.

Word for word, yes:

• de la = of the / some

But in natural English, you usually translate it as:

• some glue

That is one of those places where a literal translation is less natural than the real meaning.