This is a pretty general question, but here are some pointers to get you started:
Anything directly related to your business can be written off (as long as it is "ordinary and necessary"). If it is something that is both personal and business, then you should technically figure out what % you use it for business vs personal. For example, if you make business calls and personal calls from the same phone, and 60% of your calls are business, you can write off 60% of the phone expense. Another example: some people will take their family on vacation, and "visit their rental property," and write off most of the trip. I think this is often a very aggressive tactic, but each person has their own level of risk.
A specific example for you: if you are just competing in the competitions, then you probably can't write them off. If you are using them as a marketing or network event, then there can be opportunities to write off expenses since it would be business related.
Your understanding of tax savings is correct. Many people realize they're going to end the year in a profit situation, and hurry up to spend money. They will gladly spend $5,000 to save $1,250 in taxes (assuming 25% bracket). This makes no sense if you are buying items you don't need. If you're simply pre-purchasing items you will need anyway, then it can benefit you, depending on the extent and timing. Keep in mind you're just pulling these expenses forward a year, so you may need to find even more deductions the following year.
Losses from business activities can offset other types of income for federal purposes. State treatment will vary state to state. In PA for example, no business losses can offset wage income. If you are a Schedule C, be careful how many years you show losses, or the IRS will re-characterize it as a hobby and disallow your losses.
401k contribution limits will vary depending on your type of plan, but are limited by your wage from that entity, and/or your profit depending on how your business is set up. Gross revenues do not directly impact your contribution limits.