I always see images as a good thing for onpage optimization. You are giving your visitors visual aid to your content and therefore giving your visitors a better user experience.

Images can also hold peoples attention and make your page look more attractive and inviting, thus reducing your bounce rate.

For these reasons I am a fan of using images in my pages for SEO purposes, even if they didn't have Alt text.

No, a page with or without an image will rank just the same as long as all other things are the same (internal/external linking, etc...).

Still you can get a good amount of traffic via Google Images. I know some folks dis Google Images thinking the traffic is junk, my Adsense sites don't discriminate Google Image traffic, a click is a click.

I do suggest If you target Google Image traffic, make sure to break the Google Image frame & force the traffic to land on your page that includes the image, don't give the traffic the option to land on the direct image.

I have an old post here on WF someplace with the code to break that Google Image frame.

yes, this is the point, image can not have a direct effect on page ranking, but in a long term, it can increase the user experience of your site, which is one of the most important thing for site ranking by search engine. you can or we say, better to use it. but pay attention on the size and number.

My opinion is that if it might help though the effect might be miniscule. Again it is for a better user experience.
One tip to improve your site speed, you can host the image somewhere else instead in your website.

Another question with images... will you get penalized for duplicate image titles? Like, you have a series of sunset photos, and you title them "Sunset 1", "Sunset 2", etc?