Formal and casual talk(Japanese language hlep)?

Question:

Okay,I just started to learn speaking japanese in Casual form,there something I don't understand,look below:

Koibito ni au,jikan ga arimasen

First please translate that,thank you.

Second,the first part of the sentence is in casual form right?,and then it suddenly switch to formal at "Jikan ga arimasen",this is the part where I don't understand.

Third,I tought usually the verb is at the end of the sentence and we can't continue the word unless the verb is in "Te" form,so why is the sentence is in continuation without a fullstop.

Thanks

Answer:

"Koibito ni au (tame no) jikan ga arimasen"
I don't have time to see my girlfriend/boyfriend.

You separate the sentense wrongly. "au-jikan" is correct. (this form is called "rentaikei")

"koibitoni au" is just explaining about "time", so it doesn't need to be polite

連体形 rentaikei (Attributive form) :
is practically identical to the terminal form, but differs in use: it is prefixed to nominals and is used to define or classify the noun.

e,g. benkyou suru basho ga arimasen ("suru" is rentaikei)--> I can't find a place to study.

watashi wa koibito ni au ("au" is now terminal form) --> "watashi wa koibitoni aimasu"