Are there any other mechanisms of power?
For example, the Rules committee can classify a bill into categories. Appropriations bills, for example, are subject to different rules than general legislation.
As another example, the Rules committee determines whether a bill fits in a category that requires a supermajority vote under the House Rules (e.g. to consider a bill out of order or to suspend the rules to reconsider a bill that was previously voted upon in the current session even if its language is slightly different than another similar bill that was voted upon).
The rules committee can also decide that a bill reported out of committee needs to be referred to another committee based upon amendments made to the bill in committee.
Does the scheduling process get abused? (e.g. not scheduling)
Routinely. The scheduling process is used on a regular basis to advance the political and policy goals of the majority party, in a manner that disregards legitimate scheduling needs or the usual priorities in scheduling.
What types of rules are typically added (other than regulation of
Common rules limit the hours allowed for debate, the number of people allowed to speak on each side, the number and type of amendments allowed (and often the specific amendments that will and will not be voted upon), the maximum budget score that a bill can have and determinations of whether or not the bill complies with budget requirements or is required to, waiting periods after debate is complete before there is a final vote, waivers of the usual rules, etc.
Can the Rules Committee itself add riders?
Generally, while the Rules Committee decides what amendments will be voted upon, sometimes down to the exact wording, the Rules Committee does not generally add amendments itself.
There have been times when the Rules Committee had a practice of requiring certain kinds of legislation to have sunset provisions or certain other formalities (e.g. an effective date clause) which would have been added in to legislation lacking those clauses.
But, even then, Rules Committee imposed amendments would not be substantive, and would often require a floor vote as the first amendment to be considered in connection with the floor consideration of the legislation.
Footnote on Sourcing
This is based mostly upon my college classes on Congress, my collected gleaning from reading newspaper accounts from sources such as the Washington Post and Rollcall, and upon my recollections from when I was an intern for a member of the U.S. House of Representatives in the early 1990s. Some of my information may be outdated, although I have tried to keep abreast of this subject over the years.