It does help your other pages if you link diversified to other pages as well. So a broad base of backlinks to each page and then focusing on one at a time starting with your main keyword would be a good strategy.

No, you won't get penalized for only backlinking to one of your pages.

Building backlinks to multiple pages is preferred over just one page.

Spread your links out across your domain and you'll be fine.

No, it is not true. AT least in my personal experience, I haven't seen anything that suggests that. I have a few main page son my site, but one of them is my main page and I have been building backlinks to it for almost 3 years almost every single day and it is ranking well for its keyword. However, it would be a good idea to diversify your link building. Whether it's the anchor texts you use or the type of backlinks you build.

As far as targeting many pages for different keywords, yes, you should do that. That is what SEO is all about, ranking different pages for different keywords.

I would start with my main pages and keywords, rank them first, then move on to smaller ones. The advantage of this is that once you rank for a few big keywords, your site has some authority, so ranking for smaller keywords becomes much easier.

Of course, some would argue that it is easier to go for smaller long tail keywords first. But either way, I think it has the above mentioned benefit.

Best of luck to you.

Well I usually prefer and choose keywords for multiple pages rather than targeting different keywords for 1 page.

However I don't think you will be penalized if you target all your keywords for 1 page.

I usually focus on the homepage to start, and then after a while will start linking to the other pages. Just remember to get some diversity going with the anchor text.