I need to place a border of varying heights and widths around text. 1px #000000 is what I need.

Is there a plugin I can use or will I need to do this manually within HTML editor when editing/making a page/post?

I also need to create a calendar feature similiar to what is shown here http://www.velogirls.com/calendar.php

all depends on where you need to put it. The easiest way is to code a css selector and rule and add it to the css inserts

Well I need to place various text box sizes on 5 different static pages.

Can you provide some script? 1px and color #5A5353

here is a script for you
1) go to ato->Add HTML/CSS Inserts->CSS Inserts and add

.my_border {border: solid 3px red;}

you only do this once. You can change the parameters - go check out http://www.w3schools.com/css to find the syntax

2) each time you want a border, put <p class="my_border"> before the text and </p> at the end of the text. For example

<p class="my_border">In cursus ultricies vulputate. Phasellus congue mollis fermentum. Sed mauris odio, condimentum non mattis et, suscipit sed nibh. Nunc at turpis vitae augue adipiscing blandit eget et libero. Aenean molestie consectetur eleifend. Ut tincidunt, mi et fermentum vulputate, ante metus ultrices leo, eget interdum eros nisi sed diam. Duis vulputate arcu eu metus rutrum suscipit. Nullam ac erat eros, quis cursus lorem. Praesent non metus accumsan augue eleifend rhoncus a eget sapien. Sed tempor mollis leo id ornare. Nullam tincidunt dignissim odio, quis facilisis augue suscipit eget. Pellentesque vehicula dapibus odio, ut vestibulum sem consequat in. Sed faucibus risus quis urna scelerisque hendrerit.</p>