> Is иметь for more abstract and intangible ideas?
No. "Иметь" is direct word for "possess". But, as was said above, it sounds formal and bookish a little. Normal way to express possession is "у меня есть".
You may even think about "У меня есть книга" as "There is book of mine" - as you can note, there is no need in word "possess" to express this idea. Something similar takes place in russian. Compare to "у меня процесс занял два часа" - "Process took two hours for me" or "My process took two hours".
Also russian language tends to drop out verb "есть": "У меня два высших образования".
However, if you want to stress/emphasize idea of possession you should not omit "есть": "у меня есть" and this will be english "I have".