Pulse+Blocs is a great combo.
1) Did you "export for Pulse4 template"?
If it's missing still.. you can fix this manually.
Add this line to just before the closing
</body> in the layout.php in Template folder:
<!-- Stats Tracking Code -->
<script src="<?php echo $path; ?>/<?php echo $admin; ?>/inc/tracker.php?uri=<?php echo $_SERVER['REQUEST_URI']; ?>&ref=<?php echo $_SERVER['HTTP_REFERER']; ?>"></script>
2) Do you mean the button in Pulse is not looking the same as in Blocs? Can you share a link to the site? Which button is it? A CTA button?
It shouldn't be over-ridden by any stylings but if so it could be a quick change in the Templates style.css will do it