Can люблю also mean love?
Yes. I love my city is also accepted.
What's the difference between кохати and любити?
Кохати refers to relationship between a woman and a man, to deep feelings between them, whereas любити refers to everything. Я люблю сало, but you can't say я кохаю сало.
Depends on how weird you wanna get with that object
It should be я люблю свое місто. Maybe it's too early to teach this sort of construction.