Pantheon don't spread and have no "pressure" associated with them. Where they appear, they appear instantly and can only fade as pressure from other religions (including your own religion) convert citizens away from your pantheon to other religions.
Your pantheon will appear automatically and immediately in every city you own that does not already have a majority religion when you first adopt your pantheon belief (assuming you don't first found your pantheon when you form a religion -- that's a special case, and quite rare). So, in the ordinary case, when you select your pantheon belief you will have your capital and maybe an extra city or two -- your pantheon will automatically appear in your capital and those other cities. If you then found another city, your pantheon will automatically appear in that city as well -- until you found a religion. Once you found a religion, your pantheon is absorbed into your religion as an additional belief and your religion will automatically appear in your holy city, but will not automatically spread to existing cities or to newly founded cities. Instead, you must either manually spread your religion to your other cities (using a Great Prophet or Missionary) or let passive city-to-city pressure convert your cities (but that is slow).
As your religion spreads (and as other religions spread) to cities with a pantheon, some combination of existing pantheon followers and non-believers in that city will convert to your religion, another religion, or a combination of the two. It is not unusual that a point is reached where your pantheon is no longer majority in a city, but no religion is majority either. At that point, neither the pantheon symbol nor any religion symbol appears in that city's banner and no religious beliefs will be active in that city. So, for example, a 5-pop city that has 2 remaining pantheon followers and 2 followers of your religion, will have no religious beliefs (even though you could argue that 4 citizens are following some form of your pantheon -- 2 directly and 2 indirectly, through your religion).
I suspect this what happened in the pantheon city you gifted to another Civ -- your pantheon lost enough followers to cease being majority in that city, but no religion was yet majority either, so what you saw was a disappearing pantheon.
You may find the religion articles in the Civ 5 War Academy useful. The overview article is
here and contains links to the more detailed articles.
On your happiness question, every city you have, however you acquire it, has the same happiness cost, with one exception -- a conquered city that you have annexed will generate extra unhappiness until it has a courthouse. If you originally founded a city, gift it away and then conquer it back again, the game should recognize that as your original city and treat it as a recovered city, rather than an annexed city, but I have not tested that specific scenario. (Recapturing a city that you founded that was previously conquered and then recaptured does behave the way I describe.)
Culture cost of policies by 33% less". So, you don't get this bonus for annexed cities? ...after courthouse?
