Is home wired correctly?
Easy.   For each wire, determine if it's 10 AWG, 12 AWG, or 14 AWG wire.   Then consider the following table: 


14 AWG, 15 amp breaker
12 AWG, 20A breaker 
10 AWG, 30A breaker


Don't upsize any breakers.  But if the breaker is bigger (in amps) than the wire in the above table, downsize the breaker.  BR breakers cost $5 for a single and $10 for a double.  

Any wrong-type breakers (looking at  you Square D), replace them. 

If any cables have 2 hots (e.g. red-black-white Romex) get a 2-pole breaker of appropriate amperage and land both hots on the 2-pole.  Note a 2-pole is not a duplex. A 2-pole is twice the size of a normal breaker. 

That's it.  You're done.  

After this, some loads may trip the breaker.  If that's the case you'll have to follow the usual troubleshooting - too many loads on one circuit, too small cable needed, etc.  

If a breaker serves only one motor load, ask a new question with the motor specs and ask whether you can use (size of wire you have) with (size of breaker you used to have).