I know for certain genres, agents and publishers will only consider manuscripts that fit within their expected page count ranges. What's a good target for a standalone mystery novel? My current draft is sitting at around 70,000 words but I feel like the book would be stronger if I trimmed some of the fat.
There's not really an "ideal" count.
Harry Bingham (whose had some success in selling crime/mystery novels) suggests 75,000 - 130,000 is the norm for the genre.
Which would suggest you're in the right ballpark - perhaps even a little short. That said it would be better IMO to be a few thousand words short than to make up the numbers but sacrificing quality in the process. If you feel that the book already contains lower quality material that removing would result in improving it then you may have to experiment with removing that "fat" and if the resulting word count drops too much then you may have to look at expanding the story.
It depends. 70,000 words is an average length for most books. If you think it needs to be shortened to tighten the plot or for some other reason, I wouldn't necessarily deter you. If you are close to the stage where you would give your novel to an agent, I would be sure to ask them for their opinion. Email your agent to see what length they think would be appropriate.
A novel generally denotes a book that contains 50,000 words or more, though most on the market contain much more words.
That said, I'm going to give the same (admittedly crass but very memorable for a class of high schoolers in an all boys school) analogy of advice on proper length to use when writing anything that my High School Biology teacher gave me: "All writing should be like a girl's skirt: It should be long enough to cover everything, but short enough to keep it interesting."
I recommend you cultivate some reliable Beta Readers. I gifted my rough drafts to family at Christmas... lest you think I'm being cheap, I have a large extended family and wasn't expected to give gifts to everyone, typically just my immediate family, my cousins, and aunts and uncles... in-laws through aunts and uncles were not usually gifted with exception to two who were close to my age. So homemade was well within typical gift price range... and I would often slip the gift cards into the cover for people who I traditionally was expected to give something from... I just really hate giving gift cards and much preferred something that could be wrapped... and all books had a personalized note signed in the front cover for everyone. If you want to "steal" my strategy, it's in addition to other gifts, not a substitute for them. At any rate, family is a great way to get some feedback as you'll always have that one very critical family member who will discuss what they didn't like... but hopefully in a helpful way. I'd see what they thought was wrong and if you you ask how far they got, ask what they think... I had a few cousins finish in time to do an "ask the author" session with me before new years and give me feedback on what they liked and didn't (which was great, cause at the time, they were target audiences... The girls tended to focus on the possible romantic relationships that they saw were seeded, which helped me as I'm not someone who reads romances) while the boys tended to just confirm I was on the right track (I was writing for a teenage male audience and most of my male cousins hate reading... the worst offender finished within three days of binge reading.).