The image that says announcement is too far out
It lines up exactly with the purple banner below, but the 'design challenge' image directly below it has some (15px) padding creating space on right. My guess it that you want those to line up?
About the header image(s): these images have different dimensions which will make them shrink differently in fluid layout. If you would like them to line up horizontally on smaller screens as well I would suggest making it a single image (or use the announcement image in another place in the design.
there is more space than I want at the bottom of the paragraph element.
If you would remove that, Outlook would add it back. There are little '?' placed in the app that explain these type of things, just click it for the paragraph element to learn more about Typography in email design. I don't think there's too much space (sometime space is good ) but if you really want to do without you can use the text element (Outlook does not auto-add space for this element).
Also, I cannot find where the grey background is coming from and would like to change it to white.
There's a background applied to that row. Simply select the row and click reset icon next to the 'apply to' control to remove the row styles. You can reapply the style you do want / need.
Hope this helps!