I am not a lawyer. But the following is my understanding of current law and the licenses. It does not constitute legal advice.

To publish an app that has OGL content, the OGL content inside your app must be open source. That doesn't mean the whole app has to be open, just the files that contain OGL content. So, if you have a list of spell names, races, stats, etc. in a sqlite database or XML file in the app, you must release that sqlite database as open source under the OGL.

Note, that only one sub-race for each race, and one path/domain/option/sub-class for each class is in the SRD. If you need/want more than that, you'll need to look at other licensing options.

There is also the DM Guild, which would let you use all the content -- but you couldn't then sell it outside the Guild (which would mean a pain for people to try and get the app on a phone from there). Moreover, I don't think the Guild can handle software yet.

Lastly, a certain amount of information might possibly maybe fall allowed under Fair Use depending on usage and intent, but Fair Use is difficult and tricky beast in that you don't know if it is or isn't Fair Use until it comes before a judge and they make a ruling.

This sort of thing hasn't been gone after recently, but WoTC tends to be "moody" about their property. They will let stuff live for years without issue or action. Then, management will get squash happy again, and begin sending out DMCA notices and Cease and Desist letters. The ebbs and flows typically have a lot to do with products they are going to release. If they are about to release a product that does the same thing, they kill the competition that is in the space they want to move in. If they aren't about to release something similar, and the community is benefiting from it, they'll ignore it... Sad thing is, they will sometimes clear a space for a product, and then kill the product before release.

Yes, it can

You can make any non-magical trinket that can fit in your hand, and it disappears after the end of your next turn. One of the trinkets you can make, as listed under PHB 160, is "a whistle made from gold-colored wood" as well as "a tiny silver bell without a clapper"; these are both things that you could make such that they can fit in your hand.

Furthermore, they fit the criteria of "musical instruments," because you can make music with these. While the PHB does list some of the things it considers as instruments, it is not meant to be an exhaustive list:

Tools, PHB 154

Musical Instrument. Several of the most common types of musical instruments are shown on the table as examples.

This means prestidigitation can create a musical instrument that can fit in your hand, and you can use any musical instrument as a spellcasting focus.

Of course, it is inefficient

You must use your action to cast prestidigitation, and then you cannot use your action again to cast another spell. On your next turn, you could use the instrument to cast a spell, but then it disappears at the end of that turn, and you have to recreate it on your third turn. This allows you one spell every other round that isn't prestidigitation (unless it's a bonus action or reaction spell).