Yes, I think you’re asking about the use of this
as demonstrative pronouns.
I think this is difficult for German-speakers because you always use ‘das’ (although I believe ‘dies’ was used more in the past).
You are also right that ‘this’ is used to refer to things which are closer (whether physically, temporally or conceptually).
This is my book and that is your book. = Das (hier) ist mein Buch und das (da) ist dein Buch.
(compare with This book is mine and that book is yours. = Dieses Buch ist meins und das Buch ist deins.)
Also, this/that are only used in the singular, for plural we use these/those.
There are examples of the use of this
as a demonstrative pronoun in section II of http://de.pons.eu/dict/search/results/?q=this&l=deen&in=&lf=de&kbd=en-gb&search_in=dictionary
and for that http://de.pons.eu/dict/search/results/?q=that&l=deen&in=&lf=de&kbd=en-gb&search_in=dictionary
If you write 'This sentence...' then it usually means the sentence immediately before.