Lorentz Transforming the electric field and the change of its directions

This is a two part question about the Lorentz transformation of the electromagnetic field, the electric field to specific. The Lorentz transformation will be a simple boost in the x direction.

first question: Can I transform the Electric field without the need of Electromagnetic tensor. for example, instead of using:
$$ F^{munu} = Lambda^mu_alphaLambda^nu_beta F^{alphabeta} $$
can I use:
$$ E^mu = Lambda^mu_alpha E^alpha $$
assuming I add a zero to the electric field to turn in into 4 vector. $$ (0,E^1,E^2,E^3)$$
because when I use this approach I don’t get the relation:
$$ E^{‘}_Vert = E_Vert $$

This brings me to my second question, the last relation I mentioned doesn’t make sense to me. does it assume the x’ is in the same direction as x? isn’t Lorentz transformation basically a rotation? I can derive it easily by transforming the Tensor and getting
$$ F^{1’0′} = F^{10} $$ but this just shows that the Electric field in new coordinates in the x’ direction has the same value as the electric field in the original coordinates in the x axis right?

Sorry for the long post, I would appreciate any input!