You have problems with determiners, plurals, verb tenses, prepositions and general grammatical structure. I've corrected the first paragraph for you and highlighed problems in the second. In the second paragraph you have started inserting a space before commas, which is incorrect.

The government does not do a good job in helping the poor. According to the governments' data in 2005 , the number of  poor families has increased to 80,000 households, doubling from the 1996 figure of 40,000 households. Furthermore, some government legislation is unfair to low income groups .For example, those registered with labour unions have to pay NT$24 per month for national health insurance, (compared with average income groups - you can't say this without clearly stating the comparison. Is it double the amount average income groups pay, for example?). As a result, the gap between the poor and rich in Taiwan has extended widely since 2000.

 Recently government has focused on reducing the unemployed rate and also tried finding efficient strategies. By contrast , it seems to be fail because the unemployed rate has gone up significantly , particularly in rural areas. In addition , government opens cheaper working from south-east Asia.Therefoer companies prefer hiring those workers rather than Taiwanese.It is obviosly that government has just shown the policies about umemployed, in fact , government does not execute the policies in Taiwan.