Construct validity is a complex concept that investigates how an item actually performs in relationship to other variables. I suggest you read the Wikipedia article on this topic.
In contrast, reliability looks at the extent to which a set of items all measure the same underlying construct. The usual way to assess reliability is through Cronbach's alpha, which assumes that all of the items are scored in the same direction (i.e., negative items should be reversed).
There are five tests of validation. Three of which are what you named. Reliability is external validation --- this is a question of replicability of your findings in other studies, esp. that you are generalizing findings. Construct validity means that your constructs are actually measuring the problem, issue or phenomenon you are actually examining (example of non validity of construct: your construct for productivity is attainment of the desired outcomes of the organization in quantitative terms. but your items refer to production of outputs for each development phase. and you concluded, that there is high productivity levels for each development phase. why invalid? you did not measure outcomes). Non validity of construct may distort study findings and adversely affect reliability. However, your construct maybe found valid but you adopted either a wrong methodology or committed error in interpretation, enough to lead you to under(over)state findings. To avoid issues of construct validity and reliability, it is better to conduct a pretest of your instrument to hear from respondents what they find wrong in the items. Statistical tests can mitigate at the phase of analysis.
Reliability is not only a property of an instrument but more specifically the property of a scale used in a defined population. There are many different types of reliability used to assess the ability of an instrument to produce consistent and reproducible estimates (e.g. internal consistency, reproducibility, inter-rater, etc). See Psychometric Theory by Nunnally and Bernstein for an in depth review.
Construct validity is the concerns the relationships between the instrument (items, domains) and hypothesised external measures or characteristics of patients and patient groups - see FDA PRO guidance 2009.
Both of these psychometric properties are important in the critique of an instrument. For example an instrument can be reliable and valid, reliable but not valid (e.g. inert), or neither reliable nor valid.
Orientation of item responses (e.g. negative items) is a different matter. For whatever reason the inclusion of negative worded items into the instrument (e.g. detecting acquiescence bias). This may effect reliability if this adds an additional source of variation into the item responses. this can be tested by including method factors into the measurement model during psychometric testing.