This isn’t true at all. Solo 401ks and SEP-IRAs both allow tax-deferred savings for self-employed folks up to $55k per year, if you make enough (the amount you can contribute is a function of your profit).
Correct. My wife does this and the cap is something like 91 or 92% of gross profits. (There's a few types of tax that come out first, but it's over 90% that you can sock away if you choose.)