"I'm busy and can't make it." -- Means i know how to play, but I cannot be at your house that particular day.

Even just 'I can't make it tonight'; usually prefixed with an apology thus 'Sorry, I can't make it tonight'.
Note that for the sake of social harmony, you normally say 'sorry' even if you don't mean it; look up the phrase 'white lie'

What character should a word end with to add there "'es" instead of "'s"? I know "s" but are there any other?
Like, "Jones'es distro"
and "Arch's problems" (maybe "Arch'es problems"?).

If the distro belongs to someone names Jones, it should be Jones's distro or Jones' distro and not Jones'es distro.

If it belongs to an entire family whose members are all called Jones, it would be Joneses's distro or Joneses' distro.

Verbs that end in 'o' for eg 3rd person singular?

do => does
go => goes

Can't think of any possessives, apart from the example above.

Using Jones' as the possessive of Jones is very old-fashioned: 19th century, in fact. Write and say Jones's.

Some Classical scholars still do this with Greek and Roman names, and say Pythagoras' theorem where the rest of us say Pythagoras's. Oxford University Press advises its editors to try to discourage authors from doing it.

That is strange to me. Looks like I was learning English of 19th century... Really?
AFAIK, you can't put two "s" one after another; you can't write "Jones's", you have to put "e" between them. And who declined words ending with apostrophes? It's gone now, indeed? I can't remember last time seeing it anywhere on WWW.

Didn't realise I was that old...
I was definitely taught Pythagoras' and Jesus' and so on.
"Frankly my dear, I don't give damn"; I shall continue to do as I was taught

Re Jones + es; actually you would use 'Joneses' if referring to the family as a whole (like the 'Smiths').

I quote from the OUP Rules:

With singular nouns that end in an s sound, the extra s can be omitted if it makes the phrase difficult to pronounce (the catharsis' effects), but it is often preferable to transpose (the effects of the catharsis).

Use an apostrophe alone after singular nouns ending in an s or z sound and combined with sake: for goodness sake.

An apostrophe and s are generally used with personal names ending in an s or z sound: Bridget Jones's Diary.

Jesus's is the usual non-liturgical use; Jesus' is an accepted archaism.

Hey, I'm archaic (just Charles' thoughts -- no, it's Charles's thoughts now). I'm in good company though -- the Firefox spell-checker is archaic too

When should first letter capitals be used in a heading, name, place or title?

for example "Cureton Avenue east", or "Cureton Avenue East".

Obviously a first letter capital is noi used in "for" or "of" or "the" etc, but are there any rules.

I have Googled this question - but would like to know what this forum's members think?

For place names, capitalise the nouns and adjectives. This distinguishes those that are part of the name from those that aren't. For example "South Australia" is a specific place, but "southern Australia" is just a general area. When a name is optionally accompanied by a general term, that is not capitalised. So "the Danube" is a name in its own right, so we write "the Danube river" as opposed to "the Yellow River".

Similarly, in names of organisations, "the Royal Air Force" is a particular organisation, while "the air force" can be anybody's.

Titles are capitalised as terms of address:
"Kevin Rudd is back as prime minister." and "Kevin Rudd, the Australian prime minister..."
but
"Prime Minister Kevin Rudd said..." and "Tell me, Prime Minister, ..."

Book titles traditionally capitalise the first word, nouns, verbs, and adjectives: "The Importance of Being Ernest". Librarians, bibliographers, and some academics only capitalise the first word and proper nouns: "Linguistic typology and syntactic description". For some mysterious reason, only librarians seem to do this for periodical titles.

Hello people!

If an average native English-speaking person reads 20 of my recent posts on here, will they be able to tell if I'm a native English speaker or not?

Yes (insofar as, by "English," you mean "US 'Standard' English): Your idiom usage is incompatible there with. (E.g., most US English speakers - or writers - would shorten "my recent posts on here" to "my recent posts" or "my recent post here.")

But is “my recent posts on here” correct?