Just a few questions..

[propbeanie]

Working backwards here:
If you bring along candy canes and whiskey, you can usually keep the crew quiet - for a time anyway. Response to emergency situations may suffer, of course ...

Most of the other questions you ask would be answered based upon whether you are playing with a mod or not. Some mods have a button or hot key for you to press to ask for the "distance to empty". I do not remember if stock does though. The best speed again is mod dependent, but is generally Ahead 2/3 to Ahead Standard, so between 10-15 knots. Stock (if I remember correctly) is Ahead Standard.

Ammo for your gun is generally set, unless you use a mod for greater amounts. Generally speaking, the only way to see how much you have, and of what type, is to be at the gun station itself.

Some of the mods are notorious for problems with moving the gun. Sometimes you have no troubles. Other times, it's nothing but. Some of the issue depends upon the player, after moving the gun, to properly crew the position before leaving on patrol. However, sometimes, you do not get positions for a crew to occupy the gun, in which case, you ~know~ it's going to be messed up. I do not remember if Stock even allows you to move the gun... I gotta play Stock again sometime.

In SH4, when you get equipment varies, by chance and by location. If you are based at Pearl Harbor, you get things sooner. If you're at Fremantle, not so much. So you might get it next week (game time), or you might get it for Christmas... but "yes indeedy", the enemy can follow you, and rather closely too, if you use constant radar, though it's not put on as strongly in Stock as it is in a few of the mods. The later in the war, the better the Japanese Huff-Duff becomes, and the quicker they'll find you. Remember though, you've got radar, and you can see them coming too... give them a little surprise while you're at it...

Basically speaking, it's all down to the mods (if any) that you use.