How can the following three be done

1. Reduce the font size in chapter name in header.
2. remove subsections name appearing in the header.
4. page numbers only at the center bottom of the page and not in the header.

• Header isn't unique. Do you mean page header or chapter header? – user31729 Jan 1 '16 at 18:54
• And now add a working document as a starter please ;-) Achieving you multiple requests depends on the documentclass – user31729 Jan 1 '16 at 18:57
• You can do that with fancyhdr or, perhaps simpler to use, titletoc. – Bernard Jan 1 '16 at 20:25
• How can I bold the text in header? – user87834 Jan 2 '16 at 7:16

If this is a follow up question of Page numbers at the bottom in lyx and you want to "underline" the complete header:

\documentclass{book}
\usepackage{blindtext}% dummy text

\usepackage[