1.1. This work wants doing with great care.
1.2. This work wants to be done with great care.
Both are incorrect. You don't say 'the work wants' but 'the work needs'.
2.1. The house needs reparing.
2.2. The house needs to be repaired.
Both are correct. One is a gerund, the othe is a noun.
3.1. The dress needs washing.
3.2. The dress needs to be washed.
Both are acceptable as 2 above.
You don't say 'on the second hand' but you say 'on the other hand'.
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