Off-the-shelf is right more often than vendors admit. Custom is right when the process is the business, and bending it to fit a template costs more than building the tool.
Often, yes, and you will be told so. Custom is recommended when it is genuinely cheaper over a few years than the workarounds a product would force on you.
Yes. Most builds are integrations first: the value is usually in connecting what exists, not replacing all of it.
It is built to be handed over: documented, with your team able to maintain it or hire anyone to.