How much health do the various enemies have?

Solution 1:

Swiped directly from the Payday 2 Weapons Spreadsheet

Enemy         Health  Headshot Mul

Security        30      3.00
GenSec          50      5.00
Cop             30      3.00
FBI             50      5.00
Swat            80      4.00
Heavy Swat      100     1.67
FBI Swat        130     3.25
FBI Heavy Swat  200     2.00
Sniper          40      2.00
Shield          100     1.67
Taser           360     1.80
Bulldozer       5500    22.92
Gangster        40      4.00
Biker           80      4.00
Cloaker         320     5.33

The spreadsheet also contains a section that answers your other question about how many bullets it takes to kill any particular enemy, but it's much too complex to copy and paste here.

Keep in mind that an unaware enemy will be immediately one-shotted no matter what weapon you have equipped. Another reason to stay in stealth as long as possible.

Solution 2:

An update for newer people getting into this thread.

Some of the stats shown in this thread might have been correct for their time but for now they are incorrect which is in most cases due to balance over time from OVERKILL, the creators of the game:

The first chart with enemy hitpoints is up to date. The second one isn't, enemies don't get the 1.7x hitpoint boost. They stay at the same health as on overkill and lower difficulty. The spawns however are slightly different and there are some new enemies not listed here such as Captain Winters and his shield guards and the black dozer.

Weapons such as the heavy eagle rifle and m308 deals 80 damage, not around 40-50 damage. That means that with the 2x multiplier on the Tan you do 160 damage.