Yes. To both instances.
Commercial licenses allow you to use the font commercially. In other words, you are allowed to make money off of commercially licensed fonts. If you are charging anyone anything for the items you are creating with the fonts, you need a commercial license.
The license is granted to the individual or company purchasing the license. You are allowed to use that font as often as you want in any project you want without repurchasing. However, You are not allowed to share or give the font away for any reason. If your client wants the font, they need to purchase it (or you purchase it on their behalf).
It may be beneficial to actually read the license you get from each foundry you purchase from. Yes they are boring and tough to get through. But it may educate you considerably.