Horizontal spacing after equation

How does the following look?

\begin{align*}
  \alpha+\beta\sum_{j=1}^{m}x_{ij}  &=1&     &\text{for}\ i = 1,2,\ldots,n\\
  \sum_{i \in P_k}x_{ij}            &\leq1&  &\text{when}\ j = 1,2,\ldots,m \text{;}\ \forall k
\end{align*}

The way to have the conditions aligned is as follows:

\documentclass{scrartcl}
\usepackage{amsmath}

\begin{document}
\begin{align}
    \sum_{j=1}^{m}x_{ij} &= 1 & \text{ for } i &= 1,2,...,n
    \\
    \sum_{i \in P_k}x_{ij} &\leq 1 & \text{ for } j &= 1,2,...,m \text{; } \forall k
    \\
    \sum_{i \in P_k}x_{ij} &\leq 1 & 
    \\
    \sum_{i \in P_k}x_{ij} &\leq 1 & \text{ for } j &= 1,2,...,m \text{; } \forall k
\end{align}
\end{document}

I hope that this example answers your second question as well. Though I have no idea whether it would be possible to align everything using different align environments. As I understand, the amount of free space on the right depents on how much space do you want to leave for the conditions.

You can also use the alignat environment. It is slightly more flexible at aligning things :)

\begin{alignat}{2}
    \sum_{j=1}^{m}x_{ij} &= 1 && \text{ for } i = 1,2,...,n
    \\
    \sum_{i \in P_k}x_{ij} &\leq (1 - \sqrt{23}) && \text{ for } j = 1,2,...,m \text{; } \forall k
    \\
    \sum_{i \in P_k}x_{ij} &\leq 1 && 
    \\
    \sum_{i \in P_k}x_{ij} &\leq 1 && \text{ for } j = 1,2,...,m \text{; } \forall k
\end{alignat}

Hope that helps :) You can read about it on the amsmath documentation