hmm, well in the Character options, when the text is highlighted, there is an "Anti Aliasing" option, that you can change from smooth, to sharp, crisp, strong, and none.
But that is kind of strange you are getting that issue.
Make sure you are looking at the text at 100% zoom. I have noticed that in my designs sometimes, especially when I use OpenType PostScript (otf files).
So if you zoom at 100%, see if that is the issue first.
Also since you are working on a bigger design, you can scale the zoom down to 50%, and wont get that Jaggedy effect either, but anything in between you will...
If neither of those work, it may be a problem with the file.
If none of those work, then I dont see it working right in CSS/HTML. Did you notice it render correctly in CSS/HTML?
If so, then yeah, its the Zoom, or the Anti Aliasing.
Which Version are you using, (if you cant find anti-aliasing) I can probably explain it, but its a bit different in different versions.
But generally, its on the top, right below the main menu, a couple options right after the font size. Its a drop down box.
Good luck buddy.
As for your second question, go into the Character docklet/menu. If its not visible on the right side near your layers, then you need to enable it by selection the "typogrpahy" workflow instead of "Essentials", OR go up to the main menu, and select "Window > Character" then it should pop up.
You can do the anti aliasing there too.
But what you want to do with that, is highlight your headline, and highlight the first line of the next text.
Once you do that, go into the character window, and change the "Leading" (which is the first option on the right side. Hover over it and it will say "Change the Leading" to be sure. That is equivelent to CSS's Line Hieght.
Pretty much everything you do in Photoshop, in that character menu, you can do in CSS.
Also, if I were you, I would use pt's (points) for text. I always seem to have an offset issue with Pixels, when I transfer a design to code.
Points never let me down.
You can change your rulers, and the whole document for the rest of the design to points if you want, in the main menu, in "Edit > Preferences > Units and Rulers"
Good luck bud.