All Present & Correct - Present Tense Forms Revision

This is an example of the Present Continuous being used to suggest a time in the (fairly near) future; it carries the suggestion of several regular visits (e.g. daily, to check the pets are 'fed and watered' etc.): hence the continuous form.
If you were asking this question about people who go away on a lot of holidays (e.g. a retired couple taking frequent cruises, and who need a 'cat-sitter' several times a year, so that this is a longterm occasional habit), you would use the version in Answer 1. This is quite like asking 'Who cuts your hair?' (Suggesting that the speaker would be interested to try a haircut from this same hairdresser sometime, and perhaps become a regular customer too.)

Like many languages, English has quite a habit of telling past (or imaginary) stories in the present tense, as though they were true and happening 'right now'. We also say 'this' Irishman (or whoever) ... without it literally meaning one that the storyteller or listeners can actually see.
The second blank would be best filled by saying 'are sitting', but 'are sat' ~ using the past participal form, to describe the position they're in as a result of recently performing the action of sitting down ~ is widely heard among English speakers. ('There he was, sat in the middle of the road'; 'There she was, stood in the doorway'.)

This is an example of how the commentary (voice-over) on a wildlife documentary uses the Present Tense to describe what's happening at the same moment as we are shown it. It might also use the Present Continuous ('Because the young frog is feeling hungry, he is jumping about among the water-lilies').
Beware of the slightly irregular, but not uncommon, Present third-singular forms of verbs like 'try => tries' ( and 'fly => flies, cry => cries' etc.) and 'catch => catches' (like 'match => matches ; watch => watches', etc.).

The 'looking' is an on-going ( = continuous) process, which has already started and will presumably go on until he realises where the butter 'is'.

Answers 1 and 3 are also possible here, but slightly less natural or stylish. We do not need 'any' in the front of this sentence (as in Answer 1); but 'they eat no meat' (as in Answer 3) is good, if perhaps rather abrupt.
The phrase in Answer 4, 'I find myself hoping ... ' is a handy one to remember. ('Have you ever found yourself wondering what the world would be like if ... ?' ; 'She was left thinking about ... ' etc.)

Usually in English, someone 'does not do' something: 'We do not drive on the right-hand side of the road'; 'Britain does not have an elected President'. This is how, when discussing a fact or statement, we establish that it is NOT valid.

These are each plain true valid facts, so the Simple Present is fine to express them. We might have said 'the older people are calling it ...', which suggests that this is a temporary name that they use ('They are calling this footballer 'the new David Beckham''; 'People have started calling this 'the beginning of the end'', etc.)
Note the slight mis-spelling in Answer 2: 'referring' needs a double R in the middle.

If this is a regular bus, it comes (as a 'habit') at the same time each day; but the important thing in this situation is that the actual vehicle you want to catch is on its way right now. Hence the Present Continuous form.
Adding the 'just' gives emphasis to the fact that it is happening right now.
Note in passing that the spelling of 'coming' was wrong in Answer 4 (think about why, and check if you're not sure).

When you are stating a plain fact that is always true, you use the Simple Present in English, not the continuous form.
In this case the subject is 'two' (which in itself is a singular idea ~ perhaps slightly surprisingly!), so the verb needs to be in its third-person singular form, i.e. Answer 3 is OK while Answer 2 is not (though plenty of English speakers ~ not only children ~ might say it!).

Giving instructions (or orders) is very simple indeed in English: you just use the verb by itself as the main part of the phrase. You do not need to change its form at all, as you would in many other languages.
Don't forget that the Simple Present is all you need, without even any pronouns! (Although there is an 'indirect reflexive' in 'Pour yourself a drink' ... )