Mounting a 7-Speed Cassette on an 8/9 speed hub
Since you have friction shifters and an 8/9 speed derailleur, you should be able to pop a 9 speed cassette on the back and use the full range.  You'll have to re-adjust your limit screws of course. Worst case, if that doesn't work, you may be able to remove one of the small cogs and space it out to use only 8 speeds. 

The font chainrings will also likely be fine, usually you can go up/down one size without issue for front chainrings. Since your front chainring is designed for 8-speed, it will probably work fine with a 9-speed chain. I regularly use a 9-speed chainring in front with an otherwise all 10-speed setup without issues.