Oh of course and don’t forget handsome and impressive
Yes
On the contrary!
The OP describes a thoroughly respectable person when they are an alpha male - what you are confusing as a “douche” would be a non-alpha male unjustifiably exhibiting those traits, faking the last one. Obliviousness to the sentiments of others would be accompanied by vulnerability, so faking would be even more see-through.
The trait of “being fine with it” is perhaps the most key requirement of the role - though it must be genuine. A non-alpha male can easily claim to have the OP’s characteristics, but it will be evident whether they are sincere through the reactions of others. A sure sign that it is just a front is that people will think those traits are negative in him. A sure sign of an alpha is that people will think those traits positive, though more than likely they would be reworded to mean the same thing but in a more respectful vocabulary.
Carers, supporters, family men - these are not alphas, they are not so much attractive leaders, they are more serving. When caring is sexually attractive, tokens of care will be feigned, but only secondarily.
Alpha males are the most sexually appealing, which doesn’t necessitate being the best at bringing up the products of their sex. Caring is menial and detracts from leadership - though today we increasingly see the two coming together, as our individualistic economic system tears apart naturally healthy communal groupings. Though despite this cultural shift, alpha characteristics are not yet lost entirely.
From your need to justify why it doesn’t bother you to be “accused” of OP’s characteristics, it can be concluded that you see them in a negative light. This would be an indication that you are not genuinely fine with such accusations, especially since they have been used as accusations rather than compliments.
You are right that Alphas are plain to see just by looking at them.
They are the perfect complement to the Alpha male. The females are not defined against the males, they are mutually defined against one another. It does boil down to sexual selection in the same way for either sex - the OP’s characteristics are exhibited by the alpha male because in the alpha male they are the most sexually appealing. Likewise, alpha female characteristics are the most sexually appealing.
Propensity to care is likewise not necessitated by the alpha female role, just sexual desirability. Though in practice, the strong mother/child bond will cause the mother to be drawn to caring for their child - but this is actually a secondary issue.
Sexual selection varies according to culture and species - some contemporarily sexy attributes in human females include being fun, capable, communicatively compelling, self-confident, discriminating, and uncompromising in her choice of male - settling and submitting only to an alpha male (rather than one who inspires mothering). Though that is not to say that an alpha male is not childlike in certain ways.