Quite the opposite to the original question actually. Japanse compound verbs are generally limited to Japanese originating verbs, which are a closed class, so they are a bit limited. Furthermore, there are some limitations to how they can form. A good place to start would be Kageyama (1993; 1996). Unfortunately, these are in Japanese, but here are the references if you need:
影山太郎 (1993)『文法と語形成』東京:ひつじ書房.
影山太郎 (1996)『動詞意味論』東京:くろしお出版.
I talked about it a little bit deep in my PhD dissertation, but only in terms of motion events / change of state events. It might be enough for your purposes though:
My answer already started to answer your second question too though. Compound verbs exhibit a lot of restrictions. One is that they generally do NOT allow sino- or foreign-originating verbs, e.g.:
Furthermore, some words just colloquially allow less "combinability" (argued in my PhD thesis). For example:
Aruki-komu
? Aruki-hairu
Kake-noboru
? Hashiri-noboru
Some Japanese speakers allow the question mark sentences and others insist they can't be said (it is split). However, these are all Japanese verbs and there isn't really any good explanation I could think of other than there is some degree of colloquialness to them.
Be sure to also check Kageyama's famous restriction of transivity-harmony for Japanse compound verbs.