Scrum masters are commonly mistaken for project managers, when in fact, project managers don't really have a place in the scrum methodology. A scrum team controls its own destiny and self-organizes around their work. Agile teams use pull models where the team pulls a certain amount of work off the backlog and commits to completing it that sprint, which is very effective in maintaining quality and ensuring optimum performance of the team over the long-term. Neither scrum masters nor project managers nor product owners push work to the team (which, by contrast, tends to erode both quality and morale).
A time boxed period used to research a concept or create a simple prototype. Spikes can either be planned to take place in between sprints or, for larger teams, a spike might be accepted as one of many sprint delivery objectives. Spikes are often introduced before the delivery of large or complex product backlog items in order to secure budget, expand knowledge, or produce a proof of concept. The duration and objective(s) of a spike is agreed between product owner and development team before the start. Unlike sprint commitments, spikes may or may not deliver tangible, shippable, valuable functionality. For example, the objective of a spike might be to successfully reach a decision on a course of action. The spike is over when the time is up, not necessarily when the objective has been delivered. 
As drivendevelopment implies, the ScrumMaster is a full team member and thus should be full time. I generally treat my role as "ensuring the team functions as a well oiled machine", which can have a number of meanings at different times. Frequently, a SM spends a lot of time facilitating the team's interactions with people outside the team, especially those related to business analysis and stakeholder expectations. Beyond that, it is a matter of meeting the mechanical items listed by Cam and looking after the physical and emotional state of the team.