First, one very important aspect of the game that many people tend to overlook is the fact that is has a "looping" feature. There's no notification in the game at all that this exists, and personally, I found out completely by accident. When you get a "Game Over," the month restarts. However, you restart the month with all the Merchant Levels, Adventurer Levels, stock, pix, dungeon levels you unlocked with your previous attempt! You'll have to make your way through the Hall of Trials again, but after that, I believe you should be able to continue from the last door area again. For example, I had dungeon levels 6-11 unlocked of Jade Way during my first attempt at the second week, I got a game over, then when I restarted, I still had access to those levels. So don't stress too much about failing, just keep on trucking and don't reload your game if you want to keep your progress.
The number of customers coming in isn't really directly related to how often you open your shop. You get the peak amount of customers coming in around noon/afternoon. Business (like a real shop) is a slower in the morning and evening. So don't worry about being open "too often."
Dungeon crawling is the most optimal way to stock your shelves. Getting to the end of the dungeon means you get to take home everything instead of only one thing if you die. So survivability is your goal! Memorizing the attack patterns of the different types of enemies is definitely a good idea. If you do that, you can fairly easily get through the dungeons without taking too much damage. You can also run through the dungeons avoiding everything to get to the final boss, but you won't have as much loot to take home, so it's usually better to just kill stuff. There's also a Chain bonus which gives you bonus XP for killing monsters of the same type and color. I'm not sure if/when that bonus maxes out. It's a good way to level up your adventurer though, as well as farm on respawning enemies for some loot. Take at least one health recovery item to use in an emergency and remember, your health completely replenishes when you level. Don't rush the final bosses, take your time and watch their attack pattern if it's your first time fighting them.
The best way to get your customers to buy larger purchases is to build a better relationship with them. Customers also effectively have "levels," and whenever you sell to them, it helps go towards leveling up their relationship with you, which in turn increases their budget. Getting "Just Chains" will level up your merchant level quickly, which is when you sell something to someone without haggling. It starts out at 2XP and doing that several times in a row will give you an XP bonus up to 128 XP. This will help level up your Merchant Level quicker, which will in turn give you better options for handling your store! There is also apparently a mechanic ingame where you will gain more rep with the customer if you sell to them around or exactly at the price they were thinking of. So in general, if you're selling at a profit of 110% on a first offer rather than haggling them down to 120% after a first offer of 140%, you'll end up with better XP/Rep gain overall, even if in the short term, it's less profit.
Hope these tips help! Good luck and Capitalism, Ho!