1) I managed to convince them that insurance is THE very career path I intend to pursue. усиление - "тот самый" и индивидуализирующее определение - "I intend to pursue". 2) Little things like that make all THE difference. имеется в виду известная разница. 3) Сost of maintance can be considerable. Абстрактное существительное в общем смысле. 4) We caught /sight of a small white dot on the horizon. Абстрактное существительное в общем смысле. 5) So some people were critical of the project because of THE expense. Не любые расходы, а расходы на этот проект (по ситуации известно, какие расходы).
Last winter I visited theatre with my parents.We saw a play called "princes of snow". It was very interesting play. W had'n booked tickets in advence,so we bought tickets there.After buying tickets we went into the theatre. The hall of the theatre was full of the portraits of famous actor and actresses. Then we got into the big room. There were stalls. We took our sits. Our sits were in the middle. Our row's number was 6. It was near the aisle. We sat and waited for the performance. Suddenly the lights turned off and big curtain opened. It was wonderful! Performance last 2 hours there was a little break after first hour. When the play ended I was very happy! My family and I enjoyed too much. It was unforgotable.