Can I use -ing verbs within a sentence that's in the past tense?
Solution 1:
We consider -ing verbs to be “non-finite” verb forms. That means that they are not inflected for person or number or tense.
To carry tense, you need a finite verb form, like your continued which is the past tense of continue, and like your has which is the present tense (and third person singular) of have.
Those other verbs like loving, though, they have no tense. Use them at will with either tense.