The Inn is the hub for several important things. The Tavern (along with a Mine) is the primary requirement for Stables upgrades so its rather important to keep the Tavern caught up with your Keep level.
This is where you will find new generals to buy. The frequency of Gold Historics that appear increases as your Tavern Level increases. Usually not a good idea to waste too many gems refreshing here until after Level 27.
The dots in the Yellow Box are an indicator as to what is in your Tavern right now. With each color dot corresponding with the same color of General. Historics will be a Purple or Gold dot with a small Crown on it so they are easily recognizable. Do not waste your time buying non-Historic Generals as you will come to regret wasting time and resources on them every quickly.
The Blue Box is your Refresh or "Reroll" (you'll often heard people say that they've been "rolling in the tavern") button. For the low price of 50 gems the current Generals are dumped out of the Tavern and replaced with new ones. This is really the only way to get any decent Generals out of the Tavern because the chances of them showing up are so low that waiting out the 4 hour refresh timer will rarely if ever present you a General worth keeping.
By ticking the boxes highlighted with Red Squares you are telling the game to warn you if you are about to reroll the Tavern while there is a Gold Historic General in it. A prompt will pop up asking if you wish to continue. Having these boxes ticked allows you to very quickly "roll the tavern" and blow through a decent amount of gems in search of the General(s) that you want.
The button in the Green Box takes you to the General Portraits page. This page has every single General in it for you to examine. Separated by Culture it isn't difficult to find most Generals but sometimes it can take some searching if you're not exactly sure which Asian culture a particular General comes from. When you click on the Portrait of a General you are presented with all sorts of information like the Generals base stats and Skill. The maxed stats from the Generals Specialty are also shown along with the amount of gold required to purchase the General from the Tavern (if it is available in the Tavern). Unfortunately if a General say 'Temporarily Unavailable in the Tavern' the only way to get it is from the Top $100 pack from the . Generals under this "Temporary" status will likely never be added to the Tavern as they have been like this for years.
This is where your daily rewards come from by doing pretty much every aspect of the game. These tasks refresh daily and you need to make sure you click on the completed Activities AND the Rewards Chests above the Activity bar to claim all of your Rewards!
The last Rewards Chest is the most important as it contains 5 Runestone Chests along with a Key of Conscription that allows you to open the Great General Chest once a day.
You can click on each Activity to see exactly what needs to be done along with how many points are awarded and your current progress toward completion. Make sure to do as many as you can to get the max rewards.
Wheel of Fortune:
SPIN TO WIN BABY! The Wheel is pretty basic. For 100 coins you can spin once, or for 900 you can spin 10x all at once. By clicking the + sign in the Red Box you can purchase more coins with gems although I don't recommend this as you will get plenty of coins from general gameplay and there's not much on the Wheel worth it considering you could end up with just 10k food for your spin. By clicking on the center of the Wheel you can choose a General Blessing that modifies your Wheel for a set number of spins. The different Generals have different effects and are unlocked via VIP Levels.