Tag questions following that-clauses

John thinks that life exists on Venus, doesn't he?

shows the basic (simplified) form of the first example. The speaker is asking for confirmation of what John actually thinks.

John thinks that life exists on Venus, doesn't it?

has the wrong form for a tag-question. You'd need a separate sentence for this abrupt change of topic:

John thinks that life exists on Venus.... It does, doesn't it?

..................

I think everybody likes ice-cream, don't I?

is of the same form, but unlikely (though not impossible). There are acceptable senses, but the surface one is the speaker asking the listener to confirm (in a reaffirmation sense) what the speaker thinks ... not too likely.

I think everybody likes ice-cream, don't they?

is however available, but with the idiomatic sense

I think we can take it for read that everybody likes ice-cream.

It's really making an assertion / adding emphasis rather than asking for confirmation. A tag rhetorical question?

Just a quibble: If you don't want to say I shall, then how about simply I'll?

OK, the questions:

1.

Expects is more precise for this sense:

John expects me to help them with that work, doesn't he?

or

John expects I'll help them with that work, doesn't he?

2.

"I think everybody likes ice-cream, [doesn't he?]"

Use I think or don't they?/[doesn't he?] but not both, which would be redundant because they both signal an opinion.

I think everybody likes ice-cream.

or

Everybody likes ice-cream, doesn't he?

(I'm using the old convention of default masculine pronoun here. The current PC lexicon continues to play havoc with noun/pronoun-verb agreement.)

A statement that begins with I think (that)... is non-debatable, because no one can argue that you're not thinking what you say you're thinking, unless he claims to be a mind reader. I think (that)... is a good habit because it makes the statement less assertive or confrontational. Of course, the form may not matter for some statements:

I think you're an idiot. (Just my opinion)

You're an idiot, aren't you? (Just a question)

You're an idiot. (Just stating a fact)

...will probably get the same response.

By using tag question, a speaker wants to confirm whether his or her assertion is ok or not. Of the sentence 'I think every body likes ice-cream' speaker is 'I' and assertion is 'everybody likes ice-cream'. So we should add tag question to 'everybody likes ice-cream' and the answer might be''....., don't they?'

Of the sentence 'John thinks I will help them' speaker cannot be John, and total sentence is an assertion. So we should add tag question to the main clause 'John thinks' and the answer might be '....., doesn't he?'