You'd need to write a form for the first one. The basics:
HTML Code:
<form action="postings.php?do=domovethread&t=xxxxx" method="post" name="pulledmove" onsubmit="return confirm('Are you sure?');">
<input type="hidden" name="s" value="" />
<input type="hidden" name="securitytoken" value="xxxxxxxx" />
<input type="hidden" name="t" value="xxxxxxx" />
<input type="hidden" name="do" value="domovethread" />
<input type="hidden" name="title" value="xxxxxxx" />
<input type="hidden" name="redirect" value="xxxxxxx" />
<input type="hidden" name="redirecttitle" value="xxxxxxxx" />
<input type="hidden" name="destforumid" value="xxxxxx" /> <- You'll want this to be some dropdown to pick the forum id
<input type="submit" class="button" value="Move Thread" />
</form>
You'll need to play with that on your test site. I just use a single button to move a thread to a specific forumid on my site, so I don't use the dropdown of forumids that you'll need. But, those are the basics - you'll have to fill in the variables also.
For the second, you need to modify the CSS to not cover such a large area. Maybe something like:
HTML Code:
.postbit .posthead .nodecontrols, .postbitlegacy .posthead .nodecontrols, .eventbit .eventhead .nodecontrols {width: 50px;}
(I think there may be a fix posted in the bug report for this, so try a search in Jira.)