Answers (Remember that often there is more than one way to show that an argument is valid).
1.
1.    (F&G)v(H&-I)    (P)
2.    I-> -(F&D)         (P)
3.    -(I-> -D)             (Negation of conclusion)
4.    I                        (3)
5.    D                       (3)
6.    -(F&D)               (2,4)
7.    -F                       (5,6)
8.    F&G                   (1,4)
9.    F                        (8)
10.   -F&F                  (7,9)

2.
1.    G-> (H&-K)    (P)
2.    H <-> (L&I)    (P)
3.    -IvK                (P)
4.    G                     (Negation of conclusion)
5.    H&-K             (1,4)
6.    H                    (5)
7.    -K                   (5)
8.    L&I                 (2,6)
9.    I                     (8)
10.   -I                   (3,7)
11.  I&-I                (9,10)

3.
1.    F->(-GvH)    (P)
2.    F->G            (P)
3.    -(HvI)            (P)
4.    -(F->J)           (Negation of conclusion)
5.    F                   (4)
6.    -J                  (4)
7.    -GvH             (1,5)
8.    G                  (2,5)
9.    H                   (7,8)
10.  -H                  (3)
11.  H&-H             (9,10)

4.
1.    FvH                            (P)
2.    -H<->(LvG)                (P)
3.    (G&B)v[G&(K->G)]    (P)
4.    -F                               (Negation of conclusion)
5.    H                                (1,4)
6.    -(LvG)                        (2,5)
7.    -G                               (6)
8.    G&B                           (3,7)
9.    G                                (8)
10.   -G&G                         (7,9)

5.
1.    (-HvJ)vK                    (P)
2.    K-> -I                        (P)
3.    -[(H&I)->J]                 (Negation of conclusion)
4.    H&I                            (3)
5.    -J                                (3)
6.    H                                (4)
7.    I                                 (4)
8.    -K                              (2,7)
9.    -HvJ                            (1,8)
10.   -H                              (5,9)
11.   H&-H                          (6,10)

6.
1.    (Av-B)v-C                    (P)
2.    (DvG)vC                       (P)
3.    -{-A -> [B->(GvD)]}      (Negation of conclusion)
4.    -A                                  (3)
5.    -[B->(GvD)]                    (3)
6.    B                                    (5)
7.    -(GvD)                            (5)
8.    C                                   (2,7)
9.    Av-B                              (1,8)
10.   -B                                  (4,9)
11.  B&-B                              (6,10)

7.
1.    G&(A&N)                        (P)
2.    (A<-> -M)&(N->M)          (P)
3.    -F                                    (Negation of conclusion)
4.    G                                      (1)
5.    A                                      (1)
6.    N                                      (1)
7.    -M                                    (2,5)
8.    -N                                    (2,7)
9.    N&-N                                (6,8)