fruit or fruits?

Actually, what I'd use is the following: On the table there is some fruit.

I made an error. I meant to write "there is", but I can't edit it now.

Collo: There's some fruit on the table

We might use this construction to suggest special circumstances, depending on emphasis:

ON: Most of the fruit is under the table
TABLE: He's been looking elsewhere
ARE: The table is an unexpected place to find fruit
SOME: But most of it is found elsewhere
FRUIT: We had expected to find something else

Nat the "there" might be omitted

1) On the table are some fruit.

2) On the table are some fruits. Suggesting more than one kind

And if you omit "there" in a sentence, does it make a sentence sound more informal?

Yea Nat I'd say so, except where it's essential to the meaning

OK thank you

1) Is, definitely not are.

You have answered this question differently than others (who I agree with) here, Dale. His question is, basically, "is fruit singular or inherently plural."

Generally (maybe not "inherently") fruit is used as both singular and plural.

We normally would say "there is some fruit on the table in both of the following cases"

1. There are some apples on the table
2. There are some apples, oranges, bananas, and peaches on the table.

I have used "are," not "is" here, because I am breaking it down into individual items or categories.

But the category itself (fruit) is singular, and includes all varieties of fruit.

There are rare exceptions--i.e, where you are trying to distinguish varieties from within the class from each other, but those cases don't come up often in everyday speech.

On the table there is some fruit.
The point is moot. The verb change doesn't matter in this case. Weirdly enough, that sentence one would still be the conversationally correct.

No-one talks or writes like that. Try :

There's fruit on the table.

The fruit's on the table.