Is the personal hotspot for T-Mobile IPhone 6s free?

I have unlimited date, but I was wondering if the personal hotspot would cost any extra/make my bill higher?

No, whatever your plan has for your Hotspot limit, is the limit of your Hotspot bucket.
Hotspot data use is NEVER unlimited or free on any carrier. You get X amount (in my case 5GB of HotSpot data).

Once you use all your HotSpot data for the billing period, it is turned off, until your billing period restarts. So you won't be able to have any other device connect to the internet through your phone until then.

No, you can't do that but if you want to have a good security app do install Leo Privacy Guard in order to secure you device totally.