Not entirely sure what you mean, but I'll take a crack at explaining.

No, you do not have to buy it. You will however, have to find out which reagents have the right common traits to create the potions you want. More on that below.

Alchemy is the art of potion making and an Alchemy table can be found in most towns by a green flag and a tree like symbol. I cannot recall what the map symbol looks like, but in Davon's Watch for Ebonheart Pact players, it's right beside the Woodworking station building. You will need a solvent and two (or three, if you have the perk and wish to use it) reagents. These reagents can be harvested from nodes much like Jute fibres. For healing potions, there are, if I recall correctly, six different reagents that can be used to make "Restore Health" potions. You will need to mix any of these two reagents together in order to make such potions. Some potions also have two effects, as the reagents have more than one trait in common. So you can have the utility of two different standard potions such as Restore Health and Restore Stamina in the one vial.

Potion level is dependant on the solvent used. Natural Water for example, creates level 3 potions while Pristine Water creates level 20 potions. Solvent Proficiency requires a skill point or more to use certain types of Solvents. To level Alchemy, I found creating the highest level potion I could whilst learning the traits of reagents brought in a decent amount of experience. Once you run out of traits to learn, well; I haven't gotten that far but I imagine the next step would be to make the highest level potions (ideally ones you could sell to other players or use yourself).

As for restoring weapon enchantments, you will need a soul gem of the correct level. For example, level 11 armour will require a Minor Soul Gem to recharge the weapon to maximum capacity. To do this, right click the weapon and select "Charge" this brings up a window where you can select the soul gem in which you want to use to charge the weapon. The most efficient method of charging a weapon is to use the same level bracket gem in which the item is. However, you can use lower levelled gems... this will cost more gems than if you used the same level bracket gem. I guess this makes good use of those lower levelled gems if you don't plan on using them to revive random players in the world.

With armour enchantments though, those don't actually need to be recharged. The item itself degrades, and once it reaches 0% or damaged (as indicated by the green bar under the armour piece when you hover over it), the enchantment loses is usefulness. Repairing the item at a vendor or with a repair kit should reactivate the enchantment placed on the armour. I personally have not tried this (bit of a waste when my characters level was above the level of the armour by then), but when running around in completely damaged armour, none of the enchantments were active.

I hoped this answered your questions.

Yes if you have applied the soul trap spell (In the World skill tree)on them within the time limit (10 sec) as they die.

I think deer are too low level to fill the soul gem. you have to cast soul trap on something of the approriate level, then kill it during the spell duration. there is a passive in that skill line though that gives you a % chance to trap souls on weapon kills. I find this is more than enough while questing to keep my available gems full.

I know it is pretty tough understanding what ails me because you are all so MMO experienced and I have no/zero real experience for this MMO plus I play Solo--PvE only with no PvP intentions. Just try your best when you are up to it. Thanks.

DoT stands for Damage over Time. Skills that have this effect will apply a certain damage type after being cast and continue to apply that damage without needing to be cast again. So for example if a skill says that it will burn the target for 4 Fire Damage every 0.5 seconds for 3 seconds...then every half a second after you cast it, the target's health will be reduced by 4 (assuming they don't have any Fire Resistance). This will continue until the 3 seconds are up, having dealt 24 damage to that target's health bar. DoT can finish off an enemy. However, it can also be removed by certain skills and countered by heals.

If you're looking for some basic MMO terminology, this thread is a good place to start.

You do not have to stand there waiting for the capture. In fact you could apply Soul Trap to two enemies at once and then proceed to kill them. If you kill them both before it ends, you will have filled two soul gems. If however it takes you a bit longer and the effect wears off, you will need to cast it again on the enemy before killing it if you want to fill the gem. DoTs and debuffs (skills which hurt an enemy by reducing their resistances to damage and often are not sources of damage themselves) all have noticeable visual effects. So for instance an enemy with Fire Damage DoT will be on fire, with flames coursing over their torso. The Soul Trap visual is a bit of a blue misty glow emanating from an enemy's center. Pay attention and you should be able to spot when it wears off. Soul Trap has a distinctive noise both when you cast it and when it successfully captures a soul.