This falls in with learning the basics in design and knowing your market. Some questions you've asked should really be implemented with a vector. I would strongly know the market you are trying to design for and learn the workflow.
Examples:
Print design:
Typical resolution format is 300dpi. Photoshop can be used but should be used with minimal cases and not relied upon. I would suggest mainly using Illustrator or InDesign, vector based. Since you would be designing it in vector it can be re-sized and resolution is not an issue.
Now there are other standards we tend to fall too. If its a billboard design and won't be scene for large distances theres no reason to print @ 300 dpi and its knocked down to 150 dpi.
Web Design:
Default resolution is known as 72 dpi and even if you design at higher resolutions the browser will still only display what pixels exist and this has been discussed here. I typically do my wireframes @ the 72 dpi level but lately I have been going to straight code because designing for web is starting to become more of a problem. i say problem because what can be rendered as code is usually off to what you designed and clients are noticing and comment on this. I see and understand why some design at higher dpis for great detail but this is an area that is constantly evolving.
When I refer to learn the basics I also refer to the KISS effect. If you are going to do a full branding, such as business cards, web, etc., etc., a vector based logo can still be applied across the board. If you design in a pixel application you will spend triple time working on the resolution/quality of the artwork to look good when applied to the medium.