Top left doesn't look like a Murray. It looks like a GE maybe -- and it's an A/C unit! Alien breakers are most common on A/C units because the contractors don't care and aren't electricians.
As far as "old breakers", I have to guess that you haven't priced these breakers. You could replace the whole kaboodle for under $100 total, so why wring hands? Just replace any you don't like.
On the Square D "QO" subpanel, that panel uses a completely unique bus design that nothing else can possibly fit in. So it it is impossible to use alien breakers. Every breaker which fits in a QO panel is approved for a QO panel. (note this includes Eaton CHQ and Siemens QD types, which are made exclusively for QO panels).
As far as the QO panel maxing out the 60A breaker, how did you get that? However you got that, it's wrong. The only correct way to ascertain that is to do a Load Calculation on the panel as described in NEC Article 220. The only way that five 20's and a 15 could possibly "max out" a 60A panel is if each circuit is "maxed out" (i.e. each 20A circuit has 16A of grow lights or Bitcoin miners that are running continuously all day all night). Other than that, the breaker handles don't enter into the Load Calculation very much; you just have to crunch the numbers per Article 220 or helpful municipal worksheets that are easier to understand.
You might note that the panel is loaded lopsided; breakers 1,2,5,6 load phase L1, and breakers 2,3 load phase L2. That's not a problem; 1,2,5,6 are nowhere near overloading phase L1, but as you add additional circuits, make an effort to balance them. Panel buses are mapped like this.
One more thing, notice that with all the double-stuffs, every bus stab in the original panel has 90A or 100A stab loading (30+30+30; 30+30+20+20; 60+20+20). Be careful when arranging things, most panels have 125A stab limits.
