First - The i5-3340M is only a dual-core CPU. You're seeing four "processors" in Device Manager because you have hyperthreading enabled. Thus it can run four threads at once but the collective CPU hardware is that of two cores.
Ok, now about upgrading: The CPU on the E6530's motherboard is indeed socketed - confirmed by an eBay search for "E6530 motherboard" which finds a bunch of boards with empty CPU sockets. So a CPU upgrade is at least physically possible.
Now, to maintain compatibility with the chipset, uou need to stay within the same CPU microarchitecture and the same socket type.
Searching on Wikipedia for "i5-3340M" finds the CPU in this list. The microarchitecture is a mobile Ivy Bridge gen 3, socket type G2. (The processors shown with "BGA" designations are for directly soldering to motherboards; you don't want any of those.) The list shows only a couple of possibilities. And there are apparently no quad-core mobile Core i5's. So the best you could do with an i5 would be to increase CPU frequency from 2.7 to 2.9 GHz. Hardly worth the trouble even if the new CPU was free.
However, it's possible that a Core i7 quad would work. Core i7's are notably faster than i5's per core, and mobile quad-core are available. Generalizing from the previous article title, we look for "List of Intel Core i7 microprocessors". We're looking for mobile Ivy Bridge quad core, and the TOC guides us us to this list.
We find, for example, the i7-3740QM. Same microarch, same G2 socket, four cores (so with HT enabled can run eight threads). Again, anything in that list with the G2 socket should work.
The 3740QM does have a significantly higher TDP than your CPU (45 watts instead of 35). But it has the same built-in graphics (HD4000), and twice the L2 and L3 cache. So it would likely use battery faster and keep the fan running more, if you put all four cores to work. But if you do put all four cores (or even three) to work, you should notice a significant increase in compute throughput. (But not much in the performance of a single-threaded app. Some increase, yes, because of the increased L3 cache.)
(Going to faster quad-core CPUs in that family does not look cost-effective, based at least on their prices at release. e.g. from almost $400 to $570 to increase CPU speed from 2.7 to 2.8 GHz? Nah!)
Now, you will find used or refurbed E6530's with that i7-3740QM - so it'll probably work as a drop-in replacement. There is a faint possibility that it might not. I don't think it's a big risk, first because Dell support lists the same BIOS downloads for these machines regardless of which CPU you have; and second because Dell wants to use the same mobo for as many different CPUs as possible.
Personal experience; I've done CPU upgrades on a couple of Latitude D-series laptops and they went very well. But I can't promise that the E6530-type motherboard is as friendly. I suspect it is, again because it was very economical for Dell to be able to use the same motherboard regardless of CPU.
But the replacement CPU won't be cheap. I would search the support forums at Dell, and other forum sites, to see if you can find someone who reported success before I invested hundreds of dollars in a new CPU.
As for the SSD: Pull your hard drive. If it's a standard 9mm high 2.5 inch HD (as mine was) then virtually any SSD of the same form factor should work. If you get a thin one (7 mm high) be prepared for some difficulty getting it to plug in properly; Dell uses different "side rails" for the two heights. But it can be done.