"Dwi" is a perfectly acceptable alternative to "Dw i". I personally use "Dwi" and I believe it is more popular amongst younger people.

Indeed, both dwi and dw i are correct. I prefer dw i because it separates the verb and pronoun.

Rydw is the full word, but Welsh tends to contract everything it can! So rydw is shortened to dw. Just remember that the Welsh language is not as standardised as English (or even French). The WJEC did publish Ffurfiau Ysgrifenedig Cymraeg Llafar ['Written Forms of Spoken Welsh'] in 1991 which generally remain in force but many authors and writers still use spellings which reflect regional pronunciation. This means that the "standard" rydw is often written (and almost always spoken) as dw. Eisiau is often written (and pronounced) as isio in North Wales, and the word mofyn is often written (and pronounced) as moyn in the South. Also some words which are spelt with a silent final -f (like cyntaf, cartref) are often written without it (cynta and cartre).

You should also note that "written forms of spoken Welsh" is not the same as Literary Welsh, which is a much different thing.

Licio is just another word for "like". It's interchangeable with hoffi.

Hoffi is more a word taught in schools. First language speakers tend you say licio (North) and caru (South).