A few questions

[McCarthybrewing]

I just brewed my first batch ever. I used a starter kit for Irish red ale, I followed the instructions up until the initial gravity measuring, my brother broke the piece I needed to do that.

So first off how big of a deal is it that I have no clue where the gravity started?

Second if I bottle my beer after seven days of fermenting about how long should I wait until I taste it?

 

[Copperpots_Brewing]

Gravity readings are pretty important in brewing, however, not having one isn't going to affect the final taste. It just let you know how much sugar you extracted from grains and malt extract, and helps you predict your alcohol by volume. I assume you used an extract kit, so you don't need to worry about how much sugar you extracted from grains, you just won't have a clear number for your alcohol by volume.
If brewing is a hobby you plan to stick with, I would definitely replace your hydrometer soon.
As for bottling, you want to bottle after fermentation is completely finished, which could vary from a couple days to go over a week. As a safe bet, I would wait 10 to 14 days before bottling. That will give the yeast some time to clean up any other byproducts floating around, and improve the taste and general. Then after you add priming sugar to the wort, bottle and cap, then wait at least a week before you crack one open. You can try one every couple days, until it tastes fully carbonated. Just remember it will get better with a little bit of age.
Welcome to the addiction!

 

[BrewinHooligan]

If you brewed from a kit, used all the ingredients they supplied, and used the proper amount of water, your starting gravity is what was posted in the kit. You will want to let that beer sit more than a week before bottling, especially if you no longer have a hydrometer to make sure it is finished fermenting. 3 weeks is a much safer bet, then 3 weeks in the bottles to carb up.

 

[McCarthybrewing]

Thank you very much.

 

[Captain Damage]

1 If it's an extract based kit and the volume of beer in your fermenter is correct, then it's a pretty safe bet you are less than 1 point off of your target gravity (+/- 0.001), do don't worry about it too much.

2 You can taste it after 7 days, but it will be "green." It'll be 3 Weeks before it becomes the beer it's destined to be.

BTW most of us here would recommend not bottling until it's been in the primary fermenter for at least 2-3 weeks - especislly since your hydrometer is broken, making it hard gor you to tell if fermentation is complete