Is there any limitations on using OSM over leafletjs.com for example in my web project?
Couldn’t find the answer in wiki.
The API is largely there for OSM contributions: it is for accessing primitives to allow editing and checking of data. It is not suitable as a means of obtaining data for display purposes. Furthermore the bbox call is limited to 10k nodes of quarter of a degree square whichever is the smaller. I suspect this API does not have the type of properties you expect.
For vector data you could use an Overpass instance, which are likely to cope with larger volume traffic.
For tiles the usual rule of thumb is “if you have to ask, it is likely your usage will be deemed excessive”.
Whatever route you go, it is always wise to build in such a way that components dependent on services provided by the OSMF can readily be changed to alternative providers. That way if you end up with a lot of users you are future-proofing.