Numerals

1. Yes it is, and yes is can be pronounced with [z]. Many people just pronounce it the same as English.
2. Yes.
3. Yes, but dau is masculine and dwy is feminine. For mixed groups the masculine is used.
4. Ail and eilfed mean the same thing. You could go a long way with Welsh before ever coming across eilfed at all. It tends to be used with compound ordinals: eilfed ar bymtheg (17th - 2nd on 15) but ail ar bymtheg is common too. You’ll also see unfed instead of cyntaf in the same position. EDIT: You’ll also see ail- as a prefix which equates to English re- when it means ‘again’, e.g. ailgylchu ‘recycle’ [ail- + cylchu].
5. Yes. Why wouldn’t it be? EDIT: is this a question of cynta vs. cyntaf? If so, yes, Welsh commonly drops final -f [v] from words and sometimes they can be spelt without it too: tre(f), gorsa(f), cynta(f), etc. But if a suffix is added, the -f is restored and pronounced.
6. Officially, yes but the aspirate/spirant mutation is dying a slow death, especially for t- and p- initial words. You’ll see it more often than you’ll hear it.
7. Pump and chwech are the numbers proper. Pum and chwe are clipped versions used before a noun, it probably arose to allow the speech to flow more easily. It also occurs with cant (100) > can.
8. Yes. The -fed ordinals cause soft mutation to feminine singular noun. They also take soft mutation after the definite article: y bumed bennod ’the fifth chapter’ [< *y pumed pennod].
9. Deng is a form of deg (10) which has assimilated to a word which begins with a nasal consonant: deng mlynedd is easier to say than deg mlynedd, etc. It is only used with a few temporal words.
10. Un causes limited soft mutation to feminine nouns; dau/dwy cause soft mutation; tri (but not tair) and chwe cause aspirate/spirant mutation; saith, wyth, naw, and de(n)g cause nasal mutation (due to their historic -n terminus).
11. Yes, cyntaf follows the noun which is for reason of etymology. Cyntaf used to be an adjective and kept its adjectival position when its meaning shifted.
12. Yes. It’s not a hard-and-fast rule, but: generally after about 10 we begin to use the numeral + o + plural pattern, for smaller amounts it tends to be numeral + singular. This gets more complicated with the vigesimal compound numbers.

I can't answer all your questions but I am a bit concerned that you are studying without a grammar book. How are you learning welsh ?

The bbc has a good guide on mutations here https://www.bbc.co.uk/wales/learnwelsh/pdf/welshgrammar_mutations.pdf

and for numbers

https://www.bbc.co.uk/wales/learnwelsh/pdf/welshgrammar_e_numbers.pdf

cynta(f) is used in the spoken language, not sure what you are asking there. I would say aspirate mutation is not used as much as soft mutation in spoken welsh. I've not heard sero in welsh but there's a lot of regional variation and I don't live there.

Oh, what a can of worms.

There are three counting systems used in Welsh.

The traditional, base 20 system, which is confusing as hell. Ugain is twenty, daugain (sp?) is 2 twenties, aka 40.

The first, second, third, etc, which derive from the traditional system, but you only need to know this up to 31 for dates and times.

The modern, base 10 system that originated in Patagonia.

Once you get to the advanced level courses you’ll need to know all three.

Nobody's mentioned deufed/dwyfed. Archaic for 'second' formerly used in compound ordinals such as deufed ar bymtheg, ('seventeenth' - literally, second on fifteen). Like eilfed, you can do without it. Stick to ail in all contexts.

Sero is technical and scientific. Colloquially people say dim. Welsh does not have a Z sound and people pronounce sero as it's spelled.