Dummy vs Pipe Shoes

Ajak,
You left a lot of information out of your questions, however I can try to help with your question # 1:
"1) supporting horizontal portion of insulated pipe"
I am guessing you mean a line traveling in a pipe rack. This would be a place for a Pipe Shoe as the pipe passes each Pipe Support. If the line must leave the rack before it gets to the next support thus resulting in what amounts to a long unsupported "L" shape, then in this case you will need a Dummy Support with a Shoe under the Dummy at the appropriate support.
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"2) supporting pump piping (at horizontal straight part, not elbow point) which is insulated with adjustable support - (portion between the pipe and the base)"
What pump piping, Suction or Discharge? How long is this piping that needs support? What size is this piping that needs support? Are there Valves in this piping? Is there a Temperature issue with this piping?
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"3) supporting insulated horizontal piping (not elbow point) with spring support (variable load type)"
You do not give enough information here to be able to advise one way or another. Please describe the configuration and the situation.

Ajax,
Have you read these two articles?
pipingdesigners.com/contents/tips-tools-...pipe-supports-part-1
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pipingdesigners.com/contents/tips-tools-...pipe-supports-part-2

Ajak,
Please allow me to share with you the philosophy about Piping Job responsibilities I learned and functioned under for all of my career (1954 to 1999). You can find more about me from my profile.
A Piping Department has (or should have) five divisions or segments:
- 1. Piping Lead Engineer to run the piping groups and oversee all the piping deliverables for a given Project
- 2. Piping Material Engineers to define material types required for all the commodities on the given Project
- 3. Piping Material Control to catalog, count, requisition and control all procurement of these piping materials required on the Project
- 4. Piping Layout Designers responsible for developing Plot plans, define the proper placement of all Equipment (Pumps, Exchangers, Vessels, Heaters, etc), define the type and location of all Pipe Racks and develop the proper routing and support of all individual pipe lines on the project.
-5. Pipe Stress Engineers to perform what is in fact the first step in the total Quality Control Check of the appropriate pipe lines in accordance with the Project applicable Codes and Client Specifications

My point here is the Pipe Stress Engineer (PSE) does not determine what type support is required or where the pipe support is to be located. The PSE (and the Pipe Stress Analysis) is just a check to determines if what was done (by the qualified Piping Designer) does meet or does not meet the Project requirements.

Now, your Issue #1
It may be your common practice to include a Pipe Shoe for this application but it is not common practice to do this. Place a common Pipe Clamp collar and weld your Base Support to it. There is not enough difference in the Heat Transfer to make the added cost worthwhile.

Your Issue #2
You wrote "Since this line is subjected to stress analysis, the support location and type is based on the stress analysis results and adjustable type of support is required. "
No! The support type and location needs to be determined by the Piping Designer and the Stress Engineer should have a damn good reason for changing the type or location. Likewise the Piping Designer should have a very good reason for his/her choices and be able to defend them. The reason I stand on this position is the Piping Designer Sees a bigger picture and knows why the line is routed the way it is.

Your Issue #3
You can use a Shoe in this case OR you can use a Pipe Clamp welded to the top end plate of the Spring Support.