What can be done when a DT abuses their trust?
First you make an appeal to the individual involved either via PM, or by creating a reputation thread. If that goes nowhere the thread can serve as a discussion in the open about whether the offence deserves a negative. Following this you can appeal to individuals that have included them in their trust lists, to request they be removed. If that all fails there really isn't much to be done, people can tag freely as they see fit, it's up to the community whether they make DT or not.
And what about trust ratings that are being given for spamming?
These aren't Negative tag offences. People should if they feel it necessary tag neutral in this instance. theymos has stated spamming and such should be handled by moderators and admins.
Isn't the trust system solely for risked money purposes where we give a rating to someone when either of us risked money or got some money from the other party as loan or through any trade? Why are other things included in trust feedbacks?
Not entirely, it has to do with feedback about the individuals, or if you perceive them to be a risk to scam. Neutrals, probably my favorite admission is great for "personal" preference notations. Positives are handed out similar to negatives, more inline with I this user is a great resource or helpful to the community - though I would rather just see people include them in their trust list as opposed to just positive feedback for those cases.
Hope that helps.