Let me give you my personal opinon on these (which also reflects some of the actions I take):

1. What constitutes spam? In order to be considered spam does a bot have to post it? Is private messaging links to everyone considered spamming?

-- I consider "spam" anything that fills the forums with useless text that does not serve any purpose to the community. That includes actual spam bots, but also people who just love to create a dozen thread with not actual content other than begging for attention and in worst case talking to themselves.
Stuff that does not contain any sane topic or valuable interaction with the community.
I would consider mass-PMs with links spam, but we are not monitoring private messages (there are supposed to be private in some way after all :p) by default. So if there are complains about PM spam I'd cooperate with the players and get their permission to look at said PMs.

2. Do we even have a formalized set of forum rules? It might be worth it to create and sticky a thread detailing the rules just to be able to remind offenders. (rare though they may be.)

-- Not that I'm aware of. "The usual" netiquette applies. Basically: If you're a PITA to everyone, you'll get what you deserve :P Writing down rules is not a bad idea in general - but keep in mind that people that tend to misbehave also tend not to read (or remember) the rules - if they even care at all.

3. What is the definition of ban evasion? Is it being banned and using another account to do the exact same thing, or just a banned user creating another account at all?

-- I don't think any admin here ever mentioned ban evasion.
I personally don't care if a banned person creates a new account - especially if they better themselves. But they better don't expect any warning when they repeat doing exactly what got them banned to begin with. They will probably get banned right away again until they learn not to click the "submit" button when their post contains insults, etc.
We don't have the time to warn the same person about the same thing over and over again, while the forums get filled up with their negative posts.

I hope my answer is detailled enough for you - keep in mind there are no super strict rules - we all are humans(/sheep) and players here. It's not like we'd would immediatly instaban old members that are known for being a valuable part of the community just because they let some unniceness slip into one or two posts, etc.

If in doubt players can always contact us in live chat (or mail/PM/hw/etc.) and we'll talk about things and try to solve any problems that may exist.

PS: Well, that's embarrassing: accidently I edited your post rather than appending my answer, I couldn't restore the intro and outro, just the questions :/

  sheepluva <- me  my code stats -> 
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Your explainaaaaation is incredible, But i want to mention a few things;

1. Censoring, I like the fact that there are censored smileys which can replace my bad habit for swearing, but making this automated would help, Not against spam but making this community a happier smiley-er place

2. Abuse/Infraction Points, I understand that people have lives and familys and cannot be monitoring the forums 24/7 so i bring you Infraction points, It involves a button nderneath posts with a "report" button, The user is queried to write a breif explaination and the offender is given one abuse point, If the user gets over XX then the user will be locked until a moderator comes on

3. Post per week monitor, May help to determine spam bots quicker

Thats about it humans/sheep/bananas/chicken/lab accidents(me)/other people will be able to live in a happier community

sheepluva, I tossed in "technically ban evasion" as an offhand remark related to this. so, yeah, I kinda brought it up. Although I wasn't thinking about it as some hard and fast rule. I mean, if someone had immediately made a new account and with no visible change in behaviour it isn't like extra chances should be given to each new account. Seems to me length of time matters too.

With regards to explicit rules, seems that people who ask for explicit rules are sometimes looking to see how close to the line they can get or how they can inch around the line.

Here are the “official” rules of Hedgewars:

<<< “OFFICIAL” SEAL OF APPROVAL >>>
—Wuzzy, 11 Dec 2013

I love how the rules start with some serious commands but eventually lead to "the cake is a lie" and "there can be only one".