If you have e-SATA it is preferable to use that over the internal wiring. Though no, you will not burn anything if you try, you will need to power your 3.5'' HDD externally as it requires more voltage (and probably wattage) than your [unknown model] notebook can supply. It is recommended to use an external power supply, like one that would come with a USB/SATA adapter, but in lieu of one you may use a desktop PSU, so long as you've signaled the on-state. The simplest setup would be the following: -laptop on top of desktop case> HDD plugged into laptop SATA and desktop PSU> turn desktop on to power HDD> turn laptop on.
While I recommend using an external adapter (or simply a different partition on your laptop hard disk for your test) with a lack of e-SATA, the above should yield the result you desire.
In response to your second question, it has been common practice in the past to remove the optical drive and replace it with a HDD while replacing the motherboard drive with an SSD because SSD space has been very very expensive/byte. Keeping both allowed for the fast boot and response times of the SSD paired with the data space of a traditional hard disk. 2.5'' SSDs have the same form factor as 2.5'' HDDs and so long as their thickness is compatible, work in nearly all situations. As the cost of SSDs is dropping, more and more manufacturers and consumers are leaving the optical drives alone and replacing the HDD with large capacity solid state drives.