以下，以句子为单位做出了一定的修改，主要是表达和用法上。供参考。When I am (was)reading the advertisement(如果这是你的自荐信，此处要根据你的具体情况注明看到这则广告的具体来源), I was great（greatly） impressed by the job.I want to do something for the old(elderly).Therefore,I recommend me(myself) to you with（without） hesitation.(此处不宜用recomment这个词，可以换个表达)改：I want to do something for the elderly. Therefore, I set my heart on this perfect opportunity. I am now in the summer holidays and have enough(plenty/sufficient) time to work for you.改：I am having a summer holiday, so that time is on my side. However,I have some caring experiences because I onced looked after my grandma.改：And since I have attended my grandmother, I have sufficient knowledge regarding what older people need as well as their concerns. The most important thing is I am patient and the old in our neighborhood likes chatting with me.改:Most importantly, I am patient and the elderly in my neighborhood enjoy my company tremendously. If I am admitted,I will devote myself to take care of them. I can read newspapers to let them to learn about some latest affairs. I can do some washing,too.改：I am looking forward to spending more time with the elderly, reading newspapers to them and doing the washing for them in order to provide them with as much domestic comfort and convinence as I possibily can.
