Was the motor replaced with the same size (horsepower, amperage, voltage) motor? What is the amperage and voltage listed on the motor's data plate? In many cases the motor plate will either list the size of the required breaker, or if not, the manufacturers website will have that information available. If you "had the motor changed" it might be best to call the company that changed it and report that the new motor is tripping the breaker, where the old one did not, and have them check for issues, since they should have verified that the new motor would work the same, or made any changes needed to support any change in the motor. If you changed it yourself, that's on you.
You should not replace the breaker with a larger breaker unless the new motor requires a larger breaker.
You should not replace the breaker with a larger breaker without ALSO replacing the wire with larger wire, suited to the size of the larger breaker, which should be suited to the size of the new motor. 20 amp, 12 gauge copper, minimum - 30 amp, 10 gauge copper, minimum.
Rather than "sanding the wires" you should (with the breaker off, of course) cut off the damaged ends of the wire, pull it a little further in, and strip the ends to get new undamaged wire. If this is not possible, consider replacing the wire, especially if it's fairly short run.
110V (single-pole breaker?) is rather abnormal for most well pump installations. One potential fix would be to re-wire for 220V operation if possible
First, check out my answer to "What is a double-stuff breaker?"
Second, take a quick moment to educate yourself on "rule of six" panels. I am fairly sure you don't have one.
single pole vs tandem locations
Generally, common 1-pole breakers can go anywhere in the panel (except in Rule of Six panels in the top section, because that would put you over six).
Double-stuff breakers can only go in spaces designed for double-stuffs. A typical panel will allow this in 0, some or all of its spaces -- though "all" is becoming rare. The labeling on the panel will say where they are allowed. Newer panels also have "keying" which makes the wrong breaker impossible, though older ones do not, and there's always the wiseguy with a file defeating the keying.
do you use single until you upgrade to tandem?
Tandem is a downgrade. The breaker will perform more poorly and high loading on one side will make the other side more susceptible to nuisance trip. Much worse, double-stuffs are not available at all in AFCI or GFCI, and virtually every residential circuit today requires those. What's more, remodeling must be to new codes and that requires more circuits.
Double-stuffs are the mark of a cheap builder who decided to save $30 by buying a 20-space panel instead of the 42-space the house actually needs.
what does "circuit breaker was oversized" mean?
The breaker's job is to protect wires and devices. 14AWG wire needs 15A protection or it will overheat. Common receptacles need 20A protection or they will overheat. Certain devices need protection of a size they will specify.
An oversized breaker means somebody made a mistake, or swapped in a too-large breaker because he was overloading the circuit and got sick of the breaker tripping. Replace the correct breaker. Breakers are $5.
what's a normal breaker really called?
It's more defined by the absence of a label like duplex or quadplex. To be more specific, call it a 1-pole breaker or 2-pole breaker.
general rules?
Yah. Only use breakers listed for that panel. I certainly hope your panel is a Siemens/ITE because almost all your breakers are listed for those panels.
The Square D Homeline breaker in position 17 is the snake in the stick pile.
Now a lot of people go "oh, but they fit". Those people aren't qualified to decide whether they fit, that's UL's job. There are several brands of 1" breaker that will mutually snap in, but if you have any experience you'll notice the insertion force is all wrong. That's because the busbar blades are each shaped differently, and each breaker is made to mate with its family's busbar and not the others.
There is such a thing as a "classified breaker" made by one brand specifically for another brand's panel, but if square D made such a thing for Siemens, they would never market it as Homeline (HOM).
Best Answer
Strictly speaking, you are correct. The circuit can handle 15 A * 230 V = 3450 W before tripping*. As a safety margin, you want to stay below 80% of that, or 2760 W. Your 30 bulbs, at 75 W per bulb, draw 2250 W total, which is within the safe operating load of the circuit. So, from a physical standpoint, you're good. #14 wire is appropriate for a 15 A circuit.
However, as mentioned, you want to be aware of any local codes which limit the number of fixtures or receptacles on the circuit. As @isherwood mentions, too, you may want to consider a lower-power bulb (like LED or CFL) if it works in your situation, or an alternative lighting solution - e.g., do you really need 30 bulbs? Could you get the same result using half as many bulbs that output more light? 2200 W is a lot of power usage for lighting, so any way you can reduce that will be beneficial to your wallet :)
*In a perfect world. In the real world, breakers don't trip immediately when reaching their current limit, etc, etc.