Hi Umbi,

My responses to your questions are below:

1. Page Title on homepage:
You should be able to make this change directly in Joomla Menu Manager. Go to the menu manager and click on your home menu to edit it. Then under the Page Display Options settings, make sure Show Page Heading is set to No. See attached screenshot.

2. Left border not visible on IE:
I am not sure if you're referring to the horizontal menu at the top or the left / right sidebar menus? If its the left sidebar menu, then I think the problem is because IE does not support any CSS3 Styles (which are used to display the borders). If you want to display borders in IE 8 & 9, you can get rid of all the borders and CSS3 entries shown below:

#left .module {
	padding: 10px;
	-webkit-border-radius: 8px;
	-moz-border-radius: 8px;
	border-radius: 8px;
	border-left: 1px solid #BBB;
	border-top: 1px solid #BBB;
	-webkit-box-shadow: 0 0 2px #BEBEBE inset;
	-moz-box-shadow: 0 0 2px #BEBEBE inset;
	box-shadow: 0 0 2px #BEBEBE inset;
}

and replace it with just a solid border as shown below:

#left .module {
	padding: 10px;
	-webkit-border-radius: 8px;
	-moz-border-radius: 8px;
	border-radius: 8px;
	border: 1px solid #BBB;
}

Hope that helps!