If one person founded a company, which is an app / website, and pitch to venture capitalist, typically when are they allowed to pay themselves a salary?
founded a company, which is an app / website
No. they founded a COMPANY - that is a legal entity. It is NOT an App/Website. It HAS an App/Website. Keep simple things in life straight. A company is not an App. Ever.
typically, when are they allowed to pay themselves a salary?
Seriously, you expect founders to live on the street and eat air and drink rainwater?
Now, the salary is to be negotiated, but generally A salary is paid. Maybe not always (a rich founder may just forego that to reduce capital requirements and keep more control), but the norm will include some kind of financial remuneration being allowed.
But when the founder keeps the majority stake in their company, the normal VC practice is to base this salary on local cost of living, not on market rate for hired CEO compensation.
This is the one exception from the rule that "your salary is what you're worth to the company, not what you need". $10K a month can happen in high cost of living areas with family: it's in the investors' interest that you don't need a side job to support yourself while working on the startup.
The normal expectation is a lot lower. The investors would normally expect you to budget for yourself something comparable to what you budget for your non-engineering employees. Anything much higher will raise questions, but it's negotiable if you've got good answers.
As a side note, it's usually two people who create a company. Solo startups are hard to secure VC funding for. I've seen cases where CTO co-founders got a market rate salary, bonus and options replaced by their share. This is uncommon for non-technical founders.