What factors influence the profitability of Bitcoin mining through an app?
Note before I go further
You can not mine any meaningful Bitcoin via an app except through mainly an ASIC miner
Cause the hash needed to mine a Bitcoin can't be produced by any phone
Laptop, computer or tablet.
Now to your question
Most that make use of apps are cloud mining and the probability of seeing a legit cloud mining app is very low
And gaining a meaningful Bitcoin is almost impossible
Now the factor that might affect profitability of Bitcoin mining via app is the amount invested
The difficulty of Bitcoin at the moment
And the main mentioned by ABCbits that affects ASIC miners.
But I would advice learning about Bitcoin itself to gain a skill or sell your Service to receive BTC
Cloud mining app at there are mostly scams.
How does a mining pool differ from solo mining, and how does an app facilitate both methods?
like the name implies Mining pool simply means pooling resources together or a group adding resources together to mine Bitcoin.
Cost and returns are shared usually based on hash power generated
While solo mining means alone. Cost and returns are borne by you and you alone.
App or cloud mining has no association with solo mining in regards to Bitcoin
But mining pool do.
If it's legit? That depends
But there are more scams than good ones and even if you do find a Good one the Bitcoin mined would be negligible or the capital needed might be higher than returns.