Here to answer your questions;
Does this payment plan applies only if I get a 16gb Iphone?
I can get the 32gb Iphone for the same payment plan?
Sure, but the cash-out for the handset will definitely increase from 800/mo. to 1000/mo. or a one time charge of 24000php
Do I still have to get the Unli Surf in the Combo and the Unli Call and Texts in the Boosters or it's already with the plan and I don't have to waste any PV on those things?
UnliSurf is available as combo and can be availed (since the plan will require you to avail a mobile data subscription) inclusive with the plan. Unli Call and Text on the other hand is offered as a plan booster likewise you mentioned and is exclusive or on top of your monthly recurring fee (MRF).
I'm also concerned about the Unli LTE in my area, I live in Biñan, Laguna, and I'm worried about the internet connection. Can I use it here?
We have LTE sites in Biñan, Laguna, parts of South Luzon Expressway and Town and Country Southville Subdivision (Bulgaria St., Copenhagen St., Athens St., Berlin St, Austria St. and Geneva Street) if within those vicinities you can sure access LTE assuming that LTE is provisioned on your account as well as in your handset settings.
Will I be unable to connect to the internet without a wifi connection if we don't have LTE in our area?
In the absence of LTE, your handset will use other mobile data bands (e.g. 3G, 2G) which ever the handset's radio find reliable without ever having to connect to WiFi bands.
And also, can I pay everything in cash, including the cash out?
Certainly! Addionally, since you mentioned your a student and a postpaid subscription assumes or requires a document that supplies as your proof of income. You might want to consider paying your MRF, 6 months in advance for the application to pursue!