This site should provide you with all the information you need to answer your questions:
https://helpx.adobe.com/fonts/user-guide.html/fonts/using/font-licensing.ug.html
I think this is the answer you're looking for:
Q. Can I use Adobe fonts for commercial projects and client work?
A: Yes, Adobe's standard font licensing agreement (EULA) allows for both personal and commercial use, sales, and distribution of designs and documents which are created using the font software. This may include printed materials, logos, and rendered content like photographs, film, video and bitmap graphics.
If distributed, the design should not contain the original font, but can be converted to vector outlines, rasterized, or subsetted and embedded in an electronic document like a PDF or eBook.
Basically, as long as what you give your client cannot be edited by your client, you should be all right.
Be aware that using fonts from foundries other than Adobe might lead to a nasty suprise later on if you have to make changes. Fonts from partner font foundries can be pulled, and your only recourse then is to license the font directly from the former partner. This happened in May with Font Bureau and Carter & Cone, leading to a lot of unhappy creatives posting in this forum.