Can I factor univariate polynomials with real coefficients as a product of quadratic trinomials and binomials corresponding to the complex conjugate and real roots using Wolfram Alpha ?
If I understood you correctly, you want a factorization over the reals. One way to do this is to use decimals for your coefficients. For example, for your question you can use
Factor[x^3 - 3.0* x^2 - 2.0]
which WA will return
(1 x - 2) (1 x^2 + 1)
For the other example you tried, $x^4 - 2 x^2 + x - 2$, the command
(x - 1.49257) (x + 1.78537) (x^2 - 0.292798 x + 0.750527)
This will work well if there are only rational roots, but for irrational roots you might need to do extra work to get enough precision.
Yes, you can do it, using keyword "factor".
For example, Wolfram Alpha Pro returns for $factor x^4-2x^2+x-2:$
Putting the LHS into Wolfram Alpha gets you the form you want, about half way down the page under "Alternate forms". If that isn't what you want then I don't understand the question.