1: No, TA is not the only place to release creeps. Any island is (or will be) populatable, except for the homeland, Larkinor. It would get a bit easy if it were possible to repop monsters on the same island you catch them. Consequently: no monsters can be captured on the other islands.
2: Both influence your catch-rate. Monstalogy plays the prime role, but it to a small extent, your level affects your success-rate.
...However, at a high monsta-skill, you will already have an extreme catch-rate, level will mean little. Plus, if you have a char with high IQ/DEX/LUCK stats(generally, a semi-char), a capture will also be made more easy. This factor, however is dependant on how close these stats are compared to each other besides their actual number, so a pure fighter or mage will not recieve any bonus of substantial magnitude. A lucky mage or fighter...or a semi combateer will have a much more decent benefit-while with some application of luck as well(e.g. a first-generation messup), you've got an ultimate bonus.