(a) Using the identity \((\alpha + \beta + \gamma + \delta)^2 = \alpha^2 + \beta^2 + \gamma^2 + \delta^2 + 2(\alpha\beta + \alpha\gamma + \alpha\delta + \beta\gamma + \beta\delta + \gamma\delta)\), we have:

\(0 = \alpha^2 + \beta^2 + \gamma^2 + \delta^2 + 2(7)\)

Thus, \(\alpha^2 + \beta^2 + \gamma^2 + \delta^2 = -14\).

(b) Using the given equation, \(S_4 + 7S_2 + 3S_1 + 88 = 0\), where \(S_4 = \alpha^4 + \beta^4 + \gamma^4 + \delta^4\), we find:

\(S_4 = 10\).

(c) Expanding \((r + \alpha^2)^2 = r^2 + 2\alpha^2 r + \alpha^4\), we have:

\(\sum_{r=1}^{10} ((r + \alpha^2)^2 + (r + \beta^2)^2 + (r + \gamma^2)^2 + (r + \delta^2)^2) = \sum_{r=1}^{10} (4r^2 - 28r + 10)\)

\(= 4\left(\frac{10}{6}(10+1)(2(10)+1)\right) - 14(10)(10+1) + 10(10)\)

\(= 100\).