Can I abbreviate 'I have to' as 'I've to', please? No, don't abbreviate it. The contracted form may be acceptable in a few regional/dialect variants, but it is definitely not standard English. You can contract the 'have' to 've' if you use the 'got' form - "I've got to go" - but otherwise you need to use the full form of 'have' - "I have to go". By the way, don't forget that words ending in 'tion' are usually nouns. Note that I've corrected your question to 'Can I abbreviate..? . 'Abbreviate' is the verb.

Yes but only in certain context. In formal writing, no such abbreviation is allowed. Use them for quoted speech.

Only in certain locales. "I've to do the washing up [short for "I have to do the washing up"] before I can watch any telly" is perfectly acceptable in the UK but it might sound odd in the US. Note that "I have to" and "I've to" are not the same tense as "I have had to" and "I've had to". Different tenses are used for different purposes.

No. Not in your question. This is correct: I have had to... I've had to...