Better English

'Will' and 'Would' are modal auxiliaries. 'Would' is also the past tense of 'Will'. Though 'Would' is also used in present situation of formality.

The uses of 'Will':- for a promise, to suggest willingness, to express determination, etc.

Promise: Mary, I will always love you.
Determination: I will pass my exams by all means.
Willingness: I will do the work today.

The uses of 'Would':- it could be used in place of 'Will' to express willingness, intention and insistence. It's also used for an unrealized intention as in:

1. I would have come on time, but my car broke down on the way.
2. We would have come to the party if we were invited.

We also use 'Would' for habitual action in the past; this is what linguists call: historic present.

— Mummy would sit down and tell us long stories each and every night. (Not: mummy will.)

'There' can be an adverb, a pronoun, a preposition, an interjection and a noun. (Check the dictionary for sentence samples) while 'Their' is a determiner that indicates ownership. It could also be termed a possessive pronoun when an 's' is added. E.g: The house is theirs, not ours.

—There are five of us sir.
—There are things one should never forget in this world.
—Can you wait there for a moment?

— She loves their Gucci bags.
— He is going to destroy their plans.
— The congregation raised their hands.