There are two separate things going on here.
First off, the verb meaning "to use" is written as つかう in hiragana and 使う in kanji. There's no difference in meaning whatsoever, but this is a very common word and you're unlikely to see this verb written in hiragana outside of materials for children and Japanese learners.
When you conjugate the verb into -ている・-ています form, it looks like this:
使っている or 使っています
つかっている or つかっています
Note that when written in hiragana, the conjugation is つかっています, not つっかています.
Now, what about that word 大切? When used as a な-adjective, 大切 usually means "important," but when you use it as an adverb (by affixing に to the end before a phrase), it means "carefully." So:
使っています = I use it
大切に使っています = I use it carefully