Why do we do Hagbah, and does the congregation have to stand for Hagbah?
When the sefer torah is lifted from the bimah the tzibbur has to stand
Refer to Rashba 3:281, Radavz 6:shnei alofim 16:page 39, Elya Rabbah 149:1, Shach Y.D. 242:38, Shar Ha'tzyion 146:18, Sharei Ephraim 10:18, Sharei Chaim 10:19, Be'er Moshe 3:23:2, Yalkut Yosef 2:134:16, Yisroel B'mamadam 25:63, see Magen Avraham end of 141. One should not stand before hagbah is performed because it would not be showing respect for the sefer torah (Avnei Yusfei 1:187:2).
Taken from HALACHICALLY SPEAKING
It's generally considered respectful for the congregation to stand whenever the Torah is out but not "at rest." When it's sitting on the bima; when it's being held by someone seated (e.g. during the haftorah reading); and when it's in the Aron are all situations where it's "at rest." When it's being picked up it's not "at rest", so it's appropriate to stand for it.
And yes, everyone should be able to see the Torah.
The reason we do Hagbah is to show the congregation what parsha we are reading. For this reason, the Sephardi minhag of doing Hagbah BEFORE reading makes far more sense. Sephardim also point to exactly where we are going to read.
(Note - I am Ashkenaz)