I don't really get it how the animated weapons work... Ingame cards description is very poor.. I'm not sure if animated weapon behaves like weapon or like a creature? I.e. if my morning glory is unbreakable and cannot be stolen, will animated morning glory still will be unbreakable and won't be stolen? Can it be frozen, put into a time bubble, poisoned etc. (when it's in weapon slot, it can't)? I also noticed that my morning glory is able to break the gravity shield. Will it still be able to do that while it's animated?
Animate/Flying Weapon moves your weapon to the creature slot and then it acts as a creature.
Morningstar and Morning Glory have an inherent ability of immaterial, so when you "fly" it it will remain untargetable by spells and other abilities. But, because it is now a creature it
will become susceptible to certain shields--Ice/Permafrost (freeze), Procrastination/Turtle (delay), Fire (damage), Thorne/Spine (poisoning).
When flown a Morningstar is 7/7 and a Morning Glory is 8/4, so only the unupped is blocked by Gravity Shield.
And why upgraded photons are so good against gods? Only 1/1 each... Won't they kill me before I'll make 200 damage (or even more since gods heal to) with photons? If you mean using upgraded photons instead of light pillars then it sounds reasonable. But then I would wonder if pillars aren't more secure since they cannot be 'killed', only destroyed or stolen?
Yes they are very susceptible to damage, but if you use the Hope Shield they are very nice. You generally want to combine them with Fractal (Aether) to create a whole bunch of them. Otherwise, a split between Towers and Pendulums would be good. Pendulum is a new pillar-like permanent.
And last but not least, why would I regreat upgrading holy lights?
To get the mastery I need to use a miracle and then upgraded holy light. It's because miracle costs all light resources I have and using it leaves me with 99 hp and 0 resources. If I'd have a free healing, I'd master the fight. I think about upgrading holy light to get more money from mastering the fight, not to get better in pvp fights or gods fights. Is that a good thinking from the economic point of view or I made a mistake again? 
It is good in that sense, and if you insist on using a mono-light then it is definitely an option to upgrade. I assume what twinsbuster is referring to is that it is not a very powerful card to begin with and you are choosing to spend a lot of electrum on it. Another factor to consider is the auto-mulligan feature. What it does is if your first 7 cards do not contain a card with 0 cost (like a pillar/tower), you are automatically given another 7 cards. So if you have a no cost Holy Flash it may jeopardize your chance at getting the auto-mulligan if you don't have a pillar/tower in your initial hand.
SoD = Shard of Divinity? Sorry, I'm still a newbie 
I would highly suggest reading over the forum, especially the newbie guides, as well as the Wiki. There is a link to Wiki in the menu at the top of the screen.