If I'm connected to the Wi-Fi and to a carrier will it still use up my data plan?

I have a iPhone and use tmobile, will it use up my data if I do this? Will it use my data if I'm on airplane mode with Wi-Fi? & when I use the Wi-Fi and the carrier, will tmobile still keep record of what websites I use? Like if I go on a website can I view it online?

No it won't because you're using Wi-Fi but when you aren't then it'll use data.

No. It will not use your data plan