Are things like "Shrine of Experience" and "Leadership Flags" level dependent?

[Roman]

Do the Shrine of Experience, Statue of the Conquerer, Leadership Flags and similar map objects give experience/leadership/other benefits based on the level of the hero or is it fixed? If it is level-dependent, it would, of course, be prudent to wait until a higher level to pick them up, but if fixed, it is best to get them right away.

Also, is the experience gained from fights level dependent, or is it fixed based on the number/type of creatures defeated?

Thanks!