I'll give you my take.
How do I find out if a potential employer offers health coverage that would cover my pre-existing conditions?
As noted above this shouldn't be an issue. ACA did away with pre-ex clauses, and even before ACA, the HIPAA regs from the 90s gave full credit for meeting a pre-ex wait if covered for a minimum year with current employer.
Would a potential employer cover the medication that I need on their prescription meds plan, and at what cost to me?
Without access to the employer's health plan RX formulary, you won't know for sure. From experience, all plans I've seen will either cover the drug you mention or an equivalent. They may require yyour dependent try some other drugs (step therapy) and at least go thru prior authorization.
How do I go about researching a potential employer - would it be prior to interviews or an employment offer?
It seems to me that if you are looking at a larger employer, almost all 50+ (and most 25+) employee entities have health insurance. The outliers are those that hire lots of low wage folks: restaurants, lodging, retail, etc. If you're applying for a professional level position, almost all will offer coverage. I would make the determination based on the actual job duties and compensation, then if interested ask to review their benefit programs as part of your evaluation. If you find a position you really like, but it doesn't offer coverage, then calculate the cost to buy a plan through the marketplace (also guaranteed issue / no pre-ex due to ACA), and take that into consideration.
Is it even moral or ethical for me to seek employment with another company, knowing they will get huge insurance bills for my family?
You don't know if they will get huge bills or not. The type of claim you mention is common and most employers in the 50+ category will have one or two similar situations. For large employers, 150+, you would see very little impact. For the 500+ category, that is an insignificant claim.
If the employer is small (fewer than 50 employees), would the added insurance cost to cover my family bankrupt them, or force them to drop coverage?
Here is the way insurance works under ACA. In most states, the small group rules apply to employers with under 50 lives, the rest use 100 employees as the cut off. The vast majority of these employers now have community rates under the ACA, which means they are 100% pooled with other similar sized employers, and the medical costs from one employee have no impact on the employer's rates.
There are some exceptions - grandfathered plans (insurer can use past claims history in setting future rates), and small / medium size partial self-funded employers. This is a small subset, and usually limited to employers whose demographics (younger, especially younger males) will generate costs below the community rated ACA plans. Pre-ex is waived in these partial self-funded plans to be compliant with the ACA, but as noted above, when the employer shops for new coverage they may ask their employees to complete health questionaires, and the insurance company will use the info in rate setting.
Once above the 50 (or 100, depending on state) level, underwriting (medical conditions evaluation) is allowed for fully insured groups for rate setting.
Long answer short - No you won't bankrupt them. If they fall into the grandfathered or partial self-funded type, they can always go to the community rated ACA rates that most smaller employers already have.
Can my current employer decide to let me go because I cost so much to cover (current employer is very large and self-insured)?
Legally, no. In practical terms, very unlikely.