It's better to ask one question at a time. Multiple questions are much more likely to go unanswered and are less useful to other users with the same problems as the thread titles are too general.

But let's have a go ...

1. The mod (actually the "Sidebox for list Manufacturers logos") is defective. It's author appears to have forgotten to include the definition for BOX_MANUFACTURER_MAX_LOGOS. As a quick and dirty I recommend that you simply replace it with a numerical value in the module file.

2. This is how web pages work when refreshed.

3. Sounds like you need to turn of the alpha sorter in the Admin. Users can already sort by price, ascending or descending, by clicking on the word price in the listing title bar. You may want to add some styling or change the text to make that more obvious.

4. Insert the following into your stylesheet
.AlexaSiteStatsWidget {
display:block;
width:120px;
margin: 10px auto;
}