Before I get going, I would
strongly recommend you go to
www.dndinsider.com and grab their Character Builder tool. It's free up through 3rd level, and it will figure out all of the math and rules combinations involved in selecting powers, equipment, etc. It then generates perhaps the greatest invention in DND history: Power Cards, with all your stats, equipment, bonuses, etc, and spit out the end result as a simple "roll this for attack, this for damage" playing-card sized thing. They will seriously spoil you.
Anyway, on to your questions:
1) When my paladin uses an at-will power like Holy Strike as a minor action, I am supposed to roll Cha vs. Reflex. My Charisma is high (+3 modifier) but I am striking with my warhammer. As a dwarf with weapon training and proficiency (and a Str bonus!) I am already rolling +5 to hit. Do I take another +3 on my roll to hit because I'm using a power?
No, you're still only going to get a +5 to hit. In this case, your +5 is a combination of two things: your weapon proficiency, which is a +2 for the warhammer, and your Str bonus, which I assume is +3. Your proficiency applies to any attack rolls you make, so you will always get that +2 to hit, but your Str bonus only applies in two cases: A basic melee attack, or when a power says it's Str vs. [defense]. Since you're rolling Cha vs. Reflex, you will get +2 proficiency +3 Cha modifier, for +5.
(Quick question: How are you getting to use a standard action like Holy Strike as a minor? Is that a feat you found somewhere?)
2) Let's suppose that I do get the bonus, and I'm rolling +8 to hit against a kobold with Reflex 11... and I roll a 3. 3+8 = 11, so I... tie. Does a tie go to the attacker, the defender, or the player character?
That's an easy one: a tie on a roll is always success. If its an attack roll, the attack hits. If its a skill check, the skill succeeds. Etc. Works the same for PCs, NPCs, and monsters.
3) We were really getting beaten up, but I am a healer and should be able to fix that. When I got mobbed by the enemy, and my wife's wizard stood several squares away plinking them with magic missile and other skills, how was I supposed to get distance between me and the mob in order to safely expend a healing surge? Yes, I'm a Dwarf and a Paladin -- I can spend it as a minor action. Do I just declare that I've gained back 7hp right at the start of my turn?
No, in technical game terms, you would declare that you were using Second Wind as a minor action at any time
after the start of your turn. This is a subtle but important point: "Start of my turn" is a specific period of time that occurs before you are allowed to do anything, and is the point where most ongoing effects trigger. So, for example, if you're taking ongoing fire damage, you have to take the damage
before you can use your Second Wind.
Other then that, you can use your three actions at any time during your turn, in any order: 1 Standard, 1 Move, and 1 Minor. So you could attack, then move back, then use your Second Wind to spend a healing surge and get HP back. Or you could use Second Wind first, then move, then attack. Or whatever.
Also, because it seems you (like almost every other first-time player) may be confused by the horribly confusing healing rules: You do
not get to spend healing surges whenever you want. You have a power called Second Wind that lets you spend
one healing surge at your discretion, but once you've used that power, you cannot use it again that encounter. Instead you'd need to use other healing powers from your paladin's power list which also spend healing surges. The surge counter is basically an upper limit on how much healing your character can do in any one day, regardless of who does it.
4) When a power calls for me to tally 2[W] damage, and my base damage is 1d10+5, am I doing 2d10+5 or 2d10+10?
Your [W] damage is the damage from the PHB for that weapon type, which does not include any bonuses, just the damage dice. For a basic melee attack, you get to add your Str modifier in to the damage roll, so your base 1d10+5 is 1d10 ([W]), + 3 (Str), + 2 (your Training feat). 2[W] would be 2d10, but because you have the Training feat, you can automatically add +2 to whatever damage rolls you make, so 2[W] is 2d10+2, 5[W] is 5d10+2, etc. Then you add on any ability modifier the power calls for.
Fun Fact: Very few of the low-level paladin powers require you to be holding your Holy Symbol. You can choose instead to wield your warhammer two-handed, which gives your a +1 to your damage rolls automatically. If you need to use a power that has the "Implement" keyword (e.g. On Pain of Death), it's only a minor action to swap weapons, which you can do before you use your power.
--K