The bar area can be in front of the bathroom.

So that the bathroom takes up the wall to the left of the stairs and a bar is built in front of the bathroom. The left area becomes smaller by filling that space with the bathroom so the bar is closer to the main TV area.

Before you work on layouts, is there any plumbing in the basement now? If not, you'll have to determine how to do it and where it makes most sense. If it's a cement floor, you'll have to jackhammer it for a traditional toilet and drains. There's a system that allows you to move toilet waste and wastewater up through smaller piping but it's more costly for the equipment than traditional and it requires a dedicated electric outlet where the unit is located. Their toilet is required, but you can put any sink(s) with it. The amount of fixtures determines which unit you need. The website is www.saniflo.com. Usually you'll want to keep the new plumbing located beneath existing plumbing on the floor above to be able to tie-in.

Might be able to put bathroom in storage area and make storage over behind furnace. Tankless water heaters are great in all regards. But as Red said, definitely need licensed plumber come and assess what is doable within your budget. The plumber will also be familiar with current codes too. I see you have a sump pump, so that implies high water table? Need to make sure the plumber understands all conditions.

There is a rough in for the bathroom across the furnace but its not the best location for it as it cuts off the space :( The current storage area will have to remain storage as its low head room in that area.

There is a pipe from the 2nd floor bathroom on the top right corner and kitchen pipe on the top left corner. Where the rough in is right now, right on top of that area is the 2nd floor main bathroom.

I am afraid you are stuck with current plumbing rough ins. Or very expensive changes. There are good fixtures available for small bathrooms now that might be fun in this bathroom. Think "Tiny House". I can't tell from your drawing where these items are, so recommend getting plumber(s) to help you lay out both bathroom and wet sink/bar features. The other space should be fairly straight forward. I don't think tankless will help much because the furnace is biggest blocker. You will probably simply have to frame that off. I would start with plumbers to see what best approach is for wet areas. Then, plan around those limitations. Good luck.