I tend to use this quite a lot; It does not harm Search Engines, what is important is that only inline elements are contained within an H1 tag, that is span is a perfectly valid element, however a div is not. In your case you should use multiple spans with separate class names.

You should also consider splitting it into H1 / H2 depending on your site structure and navigation as it might make more sense in some cases.

Yes and no;

The root domain usually tends to get far more links then your inner pages, as any links about your website / brand usually come in here. Should you target keywords on the root; it would benefit from having the increased in-links.

The result would then depend on the level of on-page optimization that you are able to do on the home-page or internal page. Usually on internal pages you can control far more the content and thus make better on-page optimizations, should the levels of optimization be more or less the same I would safely assume that your home page (root) would take prominence.