For feats, most characters get a feat at first level, and then another feat at every odd-numbered level. Humans get an additional feat at first level. So, your example 5th level Elf will have 3 feats available. If you have a WOW background, think of feats as talent points - they let you customise your character a little more every couple of levels. This is spelled out in the table on p30 of the Core rulebook.
The bottom of p27 of the Advanced Player's Guide (APG) outlines how many formulae are in your book by default - at first level, you get 2 1st level, plus an extra first level for each Int modifier. At each level after first, you get another 2 formulae of any level you create. So, by 5th level, you would have 10 plus Int modifier formulae, of which up to 4 could be 2nd level formulae.
You can also use bonus elixirs each day based on your Intelligence, so you'll likely get an extra one of each level, but check the bonus spells table in the Core rulebook to be sure (not sure what your Int is).
Elixirs are totally separate to bombs, even though the rulebook confuses things by mentioning them both in the 'Alchemy' rule. The Bomb rule on p28 of the APG, halfway through first paragraph, says you can use a number of bombs per day equal to class level + Intelligence modifier.
The Brew Potion feat allows you to create a potion version of any spell in your formuale book. Think of it as making a lasting version of an extract. This is described on p551 of the Core Rulebook. You can also make alchemical items (i.e. Alchemist's Fire, acid etc), and the rules for this are covered in the Skills chapter, p.91. The items you can actually make are in the equipment chapters of the various rulebooks.
Good luck, and have fun with the alchemist.
Yes. Lab description (find it here) says:
This lab is used for making alchemical items, and provides a +2 circumstance bonus on Craft (alchemy) checks. It has no bearing on the costs related to the Craft (alchemy) skill. Without this lab, a character with the Craft (alchemy) skill is assumed to have enough tools to use the skill but not enough to get the +2 bonus that the lab provides.
So yes, even without common sense laboratory = equipment, description of what lab is ensures that it is in fact sufficient, and that it not only allows you to use alchemy, but also gives you bonus.
Equipment parts and supplies that gets used up / damaged regularly, like oil for heaters, charcoal in filters etc is included in material cost of alchemical creations already. Treat them as raw materials, because complicated, hard to get by things are made to last. And for other things like broken vials and flasks - we don't care for nicks on swords, we ignore minor damage on armor, why would we care for minor wear on lab?
Best Answer
In Pathfinder, potions are considered magic items like scrolls or wands and are made in much a similar way. Potions and oils can be made from any spell (or, if you're an Alchemist, formula) up to 3rd level with a casting time of less than one minute that affect one or more creatures.
When you make a potion, you spend material components to do so, which are represented as the gold you pay. You don't just turn the gold into a potion, you use it to purchase ingredients, containers, tools, etc. that you end up consuming when brewing a potion or oil. The value for a potion is equal to the Spell Level x Caster Level x 50 gp. When you brew a potion yourself, you divide the value in half to determine the cost of materials. For example, a Potion of Cure Moderate Wounds would cost 150 gp to make (Level 2 Spell x Minimum Caster Level 3 x 50 / 2). The ingredients themselves may vary between spells, the gold is just used as an abstraction of purchasing ingredients or the effort in finding them yourself.
You must also dedicate time to making a magic item such as a potion. In Pathfinder, potions and scrolls that cost less than 250 gp to make take 2 hours. All other magic items (including potions worth more than 250 gp) take 8 hours for every 1,000 gp of their base price (before you divide it in half for materials) with a minimum of 8 hours. The Potion of Cure Moderate Wounds mentioned earlier would therefore take 8 hours to brew (because its base price is 300 gp, which is more than 250 gp).
To brew the potion, you must work in a place without distractions for up to 8 hours/day. You can work while adventuring for 4 hours/day, but it only counts as 2 hours of work. Otherwise you work in 4 hour blocks that cannot be interrupted in a quiet place with the tools necessary to make the item. You make a skill check (Spellcraft or Craft (alchemy) for potions) versus a DC of 5 + Caster Level of the item. Failing means the materials are wasted and the process must start again. Failing by 5 or more creates a cursed item. You can only work on one magic item at a time.
You must prepare or have the ability to prepare the spell required for the potion (so you cannot brew a potion if you have no available spell slots). You can use any Caster Level between the minimum required for the spell ((2 x Spell Level) - 1, usually) and your Caster Level, though it will change the price of the ingredients required. Brewing a potion consumes the spell slot the spell was prepared in, and any material component costs are added to the cost of ingredients, i.e. a potion that costs 150 gp for magical ingredients and 300 gp for its material components would cost 450 gp to brew.
Brewing potions requires the Brew Potion feat. Once a potion is brewed successfully, it lasts until it's imbided or is dispelled by other means. Potions don't have expiration dates.
In summary, to brew a potion you have to do the following: