If I am davening Shachris and I am slower than the tzibur and I want to start Shemoneh Esrei with them, can i go ahead of the tzibur and start to say the brachos of shema (while they are saying pesukei d’zimra) and answer to Barchu, if i am saying the brachos before shema?
You definitely can start saying birkas kriyas shema before the tzibbur starts it, in order to start shemona esrei together with them. I personally heard from R’ Volbe zt”l (Mirrer Yeshiva in Yerushalayim) numerous times that when a yeshiva person is davening in a quick minyan that this is precisely what he should do.
You just have to be careful that if you are in middle of a bracha, you may only talk out for certain things. What is applicable for your situation is that you may answer amen after the words “da’amiron b’olma) at the end of the half kaddish beore borchu, the amen of yehei shmei rabba, yehei shmei rabba and borchu. Other things that the tzibur will be saying then may not be answered. Between brachos you may also answer amein to yishtabach. It is important to know that bracha of Yotzer hameoros is from after borchu until yoter hameoros.
It would be advisable for you to learn Orach Chayim siman 66 for more details.
M:B 66-17, 18,19