An AMI, as you note, is a machine image. It's a total snapshot of a system stored as an image that can be launched as an instance. We'll get back to AMIs in a second.
Lets look at EBS. Your other two items are sub-items of this. EBS is a virtual block device. You can think of it as a hard drive, although it's really a bunch of software magic to link into another kind of storage device but make it look like a hard drive to an instance.
EBS is just the name for the whole service. Inside of EBS you have what are called volumes. These are the "unit" amazon is selling you. You create a volume and they allocate you X number of gigabytes and you use it like a hard drive that you can plug into any of your running computers (instances). Volumes can either be created blank or from a snapshot copy of previous volume, which brings us to the next topic.
Snapshots are ... well ... snapshots of volumes: an exact capture of what a volume looked like at a particular moment in time, including all its data. You could have a volume, attach it to your instance, fill it up with stuff, then snapshot it, but keep using it. The volume contents would keep changing as you used it as a file system but the snapshot would be frozen in time. You could create a new volume using this snapshot as a base. The new volume would look exactly like your first disk did when you took the snapshot. You could start using the new volume in place of the old one to roll-back your data, or maybe attach the same data set to a second machine. You can keep taking snapshots of volumes at any point in time. It's like a freeze-frame instance backup that can then easy be made into a new live disk (volume) whenever you need it.
So volumes can be based on new blank space or on a snapshot. Got that? Volumes can be attached and detached from any instances, but only connected to one instance at a time, just like the physical disk that they are a virtual abstraction of.
Now back to AMIs. These are tricky because there are two types. One creates an ephemeral instances where the root files system looks like a drive to the computer but actually sits in memory somewhere and vaporizes the minute it stops being used. The other kind is called an EBS backed instance. This means that when your instances loads up, it loads its root file system onto a new EBS volume, basically layering the EC2 virtual machine technology on top of their EBS technology. A regular EBS volume is something that sits next to EC2 and can be attached, but an EBS backed instance also IS a volume itself.
A regular AMI is just a big chunk of data that gets loaded up as a machine. An EBS backed AMI will get loaded up onto an EBS volume, so you can shut it down and it will start back up from where you left off just like a real disk would.
Now put it all together. If an instance is EBS backed, you can also snapshot it. Basically this does exactly what a regular snapshot would ... a freeze frame of the root disk of your computer at a moment in time. In practice, it does two things different. One is it shuts down your instance so that you get a copy of the disk as it would look to an OFF computer, not an ON one. This makes it easier to boot up :) So when you snapshot an instance, it shuts it down, takes the disk picture, then starts up again. Secondly, it saves that images as an AMI instead of as a regular disk snapshot. Basically it's a bootable snapshot of a volume.
You list "1690 GB of instance storage". It isn't clear if you were just quoting the specs of your instance type or if you have actually formatted and are using all that storage.
It isn't clear from the question exactly what storage you want to increase. Here are some thoughts on different situations:
It is not possible to increase instance-store beyond the limit you quote. However, by default, that storage is not all formatted and mounted on the instance, so you could get up to that limit as long as you wanted to use instance-store. Be aware, that instance-store disk is ephemeral and the contents are lost when the instance is stopped, terminated, or fails.
If your instance itself is running on an instance-store root disk, then you cannot increase the size of the root disk without starting another instance, and even then, instance-store root disks have a hard limit of 10GB on EC2.
It is possible to create and attach EBS volumes to either instance-store or EBS boot instances if you simply want to add space and move your data there (recommended). It is also possible to increase the size of attached EBS volumes up to a limit of 1TB (and beyond using RAID0 of multiple EBS volumes).
All that said, I'm going to guess that the most likely situation you're in is that you are running an EBS boot instance and need to increase the size of the EBS boot volume.
You can increase the size of an EBS boot volume without control panel access (email/password for Amazon account), however you will need to have access to the AWS credentials in order to create snapshots and volumes, to detach and attach volumes, and to stop and start the instance. You will also need ssh access in order to resize the filesystem on the larger EBS volume.
Here's an article I wrote about this process:
Resizing the Root Disk on a Running EBS Boot EC2 Instance
http://alestic.com/2010/02/ec2-resize-running-ebs-root
In related topic to permissions, here's an article I wrote explaining the different types of AWS credentials:
Understanding Access Credentials for AWS/EC2
http://alestic.com/2009/11/ec2-credentials
Providing more details in your question about your situation and what you want to accomplish would help improve the relevance of the answers.
Best Answer
lscpuorcat /proc/cpuinfoshould have what you need.